LMFDB - Embedded newform 361.2.e.b.234.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,3,-9,3,3,0,-6,-15,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			234.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	361.234
Dual form			361.2.e.b.54.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.673648 + 0.565258i) q^{2} +(0.500000 + 0.181985i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(-0.439693 - 2.49362i) q^{5} +(-0.439693 + 0.160035i) q^{6} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-2.08125 - 1.74638i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(-0.326352 + 0.565258i) q^{12} +(-4.97178 + 1.80958i) q^{13} +(0.286989 + 1.62760i) q^{14} +(0.233956 - 1.32683i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(1.26604 - 1.06234i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(0.766044 - 0.642788i) q^{21} +(2.81908 + 1.02606i) q^{22} +(0.305407 - 1.73205i) q^{23} +(-0.262174 - 1.48686i) q^{24} +(-1.32635 + 0.482753i) q^{25} +(2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(1.76604 + 1.48189i) q^{28} +(2.65657 + 2.22913i) q^{29} +(0.592396 + 1.02606i) q^{30} +(0.971782 - 1.68317i) q^{31} +(5.29813 - 1.92836i) q^{32} +(-0.315207 - 1.78763i) q^{33} +(-0.252374 + 1.43128i) q^{34} +(-4.47178 - 1.62760i) q^{35} +(2.55303 - 2.14225i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(-5.50387 + 4.61830i) q^{40} +(-4.21941 - 1.53574i) q^{41} +(-0.152704 + 0.866025i) q^{42} +(0.833626 + 4.72773i) q^{43} +(3.93242 - 1.43128i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(0.773318 + 1.33943i) q^{46} +(0.549163 + 0.460802i) q^{47} +(0.0170741 + 0.0143269i) q^{48} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(0.826352 - 0.300767i) q^{51} +(-1.12701 - 6.39160i) q^{52} +(1.06031 - 6.01330i) q^{53} +(2.51367 + 0.914901i) q^{54} +(-6.61721 + 5.55250i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(8.24170 - 6.91560i) q^{59} +(1.55303 + 0.565258i) q^{60} +(0.762174 - 4.32250i) q^{61} +(0.296789 + 1.68317i) q^{62} +(-4.79813 + 1.74638i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(1.22281 + 1.02606i) q^{66} +(-10.8871 - 9.13538i) q^{67} +(1.01367 + 1.75573i) q^{68} +(0.467911 - 0.810446i) q^{69} +(3.93242 - 1.43128i) q^{70} +(2.38919 + 13.5497i) q^{71} +(-1.33868 + 7.59202i) q^{72} +(7.06418 + 2.57115i) q^{73} +(-0.564178 + 0.473401i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(1.89646 - 1.59132i) q^{78} +(-6.54323 - 2.38154i) q^{79} +(0.0184183 - 0.104455i) q^{80} +(1.13429 + 6.43285i) q^{81} +(3.71048 - 1.35051i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(0.613341 + 1.06234i) q^{84} +(-3.20574 - 2.68993i) q^{85} +(-3.23396 - 2.71361i) q^{86} +(0.922618 + 1.59802i) q^{87} +(-4.84002 + 8.38316i) q^{88} +(-2.14543 + 0.780873i) q^{89} +(-1.05051 - 5.95772i) q^{90} +(-1.72668 + 9.79250i) q^{91} +(2.02734 + 0.737892i) q^{92} +(0.792204 - 0.664738i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(1.39646 - 1.17177i) q^{97} +(-2.86571 - 1.04303i) q^{98} +(-1.60947 + 9.12776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{8} - 15 q^{9} - 3 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 9 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26}+ \cdots - 27 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^8 - 15 * q^9 - 3 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 9 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 9 * q^31 + 18 * q^32 - 9 * q^33 - 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 - 9 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 + 18 * q^46 + 15 * q^47 + 21 * q^48 + 15 * q^49 + 15 * q^50 + 6 * q^51 + 21 * q^52 + 12 * q^53 - 6 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 + 12 * q^65 + 18 * q^66 - 6 * q^67 - 15 * q^68 + 12 * q^69 + 6 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 - 30 * q^75 - 18 * q^77 + 21 * q^78 - 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 - 3 * q^84 - 9 * q^85 - 24 * q^86 - 21 * q^87 - 9 * q^88 + 3 * q^89 - 9 * q^90 + 3 * q^91 - 30 * q^92 - 36 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^97 - 27 * q^98 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.673648	+	0.565258i	−0.476341	+	0.399698i	−0.849101	−	0.528230i	$-0.822856\pi$
$2$	−0.673648	+	0.565258i	−0.476341	+	0.399698i	0.372760	+	0.927928i	$0.378411\pi$
$3$	0.500000	+	0.181985i	0.288675	+	0.105069i	0.482299	−	0.876007i	$-0.339802\pi$
$3$	0.500000	+	0.181985i	0.288675	+	0.105069i	−0.193624	+	0.981076i	$0.562024\pi$
$4$	−0.213011	+	1.20805i	−0.106506	+	0.604023i
$5$	−0.439693	−	2.49362i	−0.196637	−	1.11518i	−0.910069	−	0.414457i	$-0.863972\pi$
$5$	−0.439693	−	2.49362i	−0.196637	−	1.11518i	0.713432	−	0.700724i	$-0.247140\pi$
$6$	−0.439693	+	0.160035i	−0.179504	+	0.0653340i
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	−0.631977	−	0.774987i	$-0.717756\pi$
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	0.987147	+	0.159814i	$0.0510895\pi$
$8$	−1.41875	−	2.45734i	−0.501603	−	0.868802i
$9$	−2.08125	−	1.74638i	−0.693751	−	0.582126i
$10$	1.70574	+	1.43128i	0.539401	+	0.452612i
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$	−0.326352	+	0.565258i	−0.0942097	+	0.163176i
$13$	−4.97178	+	1.80958i	−1.37892	+	0.501887i	−0.921852	−	0.387542i	$-0.873324\pi$
$13$	−4.97178	+	1.80958i	−1.37892	+	0.501887i	−0.457072	+	0.889430i	$0.651102\pi$
$14$	0.286989	+	1.62760i	0.0767010	+	0.434993i
$15$	0.233956	−	1.32683i	0.0604071	−	0.342585i
$16$	0.0393628	+	0.0143269i	0.00984071	+	0.00358173i
$17$	1.26604	−	1.06234i	0.307061	−	0.257655i	−0.476215	−	0.879329i	$-0.657992\pi$
$17$	1.26604	−	1.06234i	0.307061	−	0.257655i	0.783276	+	0.621674i	$0.213547\pi$
$18$	2.38919			0.563136
$19$		0			0
$19$		0			0
$20$	3.10607			0.694538
$21$	0.766044	−	0.642788i	0.167165	−	0.140268i
$22$	2.81908	+	1.02606i	0.601029	+	0.218757i
$23$	0.305407	−	1.73205i	0.0636818	−	0.361158i	−0.936269	−	0.351283i	$-0.885746\pi$
$23$	0.305407	−	1.73205i	0.0636818	−	0.361158i	0.999951	−	0.00987481i	$-0.00314330\pi$
$24$	−0.262174	−	1.48686i	−0.0535161	−	0.303505i
$25$	−1.32635	+	0.482753i	−0.265270	+	0.0965505i
$26$	2.32635	−	4.02936i	0.456235	−	0.790222i
$27$	−1.52094	−	2.63435i	−0.292706	−	0.506982i
$28$	1.76604	+	1.48189i	0.333751	+	0.280050i
$29$	2.65657	+	2.22913i	0.493313	+	0.413939i	0.855212	−	0.518278i	$-0.173427\pi$
$29$	2.65657	+	2.22913i	0.493313	+	0.413939i	−0.361899	+	0.932217i	$0.617871\pi$
$30$	0.592396	+	1.02606i	0.108156	+	0.187332i
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	−0.765464	−	0.643479i	$-0.777490\pi$
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	0.940001	+	0.341172i	$0.110824\pi$
$32$	5.29813	−	1.92836i	0.936587	−	0.340890i
$33$	−0.315207	−	1.78763i	−0.0548706	−	0.311187i
$34$	−0.252374	+	1.43128i	−0.0432818	+	0.245463i
$35$	−4.47178	−	1.62760i	−0.755869	−	0.275114i
$36$	2.55303	−	2.14225i	0.425506	−	0.357042i
$37$	0.837496			0.137684			0.0688418	−	0.997628i	$-0.478070\pi$
$37$	0.837496			0.137684			0.0688418	+	0.997628i	$0.478070\pi$
$38$		0			0
$39$	−2.81521			−0.450794
$40$	−5.50387	+	4.61830i	−0.870238	+	0.730217i
$41$	−4.21941	−	1.53574i	−0.658961	−	0.239842i	−0.00917315	−	0.999958i	$-0.502920\pi$
$41$	−4.21941	−	1.53574i	−0.658961	−	0.239842i	−0.649788	+	0.760116i	$0.725142\pi$
$42$	−0.152704	+	0.866025i	−0.0235627	+	0.133631i
$43$	0.833626	+	4.72773i	0.127127	+	0.720972i	0.980022	+	0.198889i	$0.0637335\pi$
$43$	0.833626	+	4.72773i	0.127127	+	0.720972i	−0.852895	+	0.522082i	$0.825155\pi$
$44$	3.93242	−	1.43128i	0.592834	−	0.215774i
$45$	−3.43969	+	5.95772i	−0.512759	+	0.888125i
$46$	0.773318	+	1.33943i	0.114020	+	0.197488i
$47$	0.549163	+	0.460802i	0.0801037	+	0.0672150i	0.681960	−	0.731389i	$-0.261128\pi$
$47$	0.549163	+	0.460802i	0.0801037	+	0.0672150i	−0.601857	+	0.798604i	$0.705572\pi$
$48$	0.0170741	+	0.0143269i	0.00246444	+	0.00206791i
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$	0.620615	−	1.07494i	0.0877682	−	0.152019i
$51$	0.826352	−	0.300767i	0.115712	−	0.0421159i
$52$	−1.12701	−	6.39160i	−0.156288	−	0.886355i
$53$	1.06031	−	6.01330i	0.145644	−	0.825991i	−0.821203	−	0.570636i	$-0.806697\pi$
$53$	1.06031	−	6.01330i	0.145644	−	0.825991i	0.966847	−	0.255354i	$-0.0821922\pi$
$54$	2.51367	+	0.914901i	0.342067	+	0.124502i
$55$	−6.61721	+	5.55250i	−0.892265	+	0.748699i
$56$	−5.33275			−0.712618
$57$		0			0
$58$	−3.04963			−0.400436
$59$	8.24170	−	6.91560i	1.07298	−	0.900335i	0.0776586	−	0.996980i	$-0.475256\pi$
$59$	8.24170	−	6.91560i	1.07298	−	0.900335i	0.995319	+	0.0966450i	$0.0308112\pi$
$60$	1.55303	+	0.565258i	0.200496	+	0.0729745i
$61$	0.762174	−	4.32250i	0.0975864	−	0.553440i	−0.896338	−	0.443372i	$-0.853782\pi$
$61$	0.762174	−	4.32250i	0.0975864	−	0.553440i	0.993924	−	0.110068i	$-0.0351068\pi$
$62$	0.296789	+	1.68317i	0.0376923	+	0.213763i
$63$	−4.79813	+	1.74638i	−0.604508	+	0.220023i
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	6.69846	+	11.6021i	0.830842	+	1.43906i
$66$	1.22281	+	1.02606i	0.150518	+	0.126299i
$67$	−10.8871	−	9.13538i	−1.33007	−	1.11606i	−0.984060	−	0.177835i	$-0.943091\pi$
$67$	−10.8871	−	9.13538i	−1.33007	−	1.11606i	−0.346014	−	0.938229i	$-0.612465\pi$
$68$	1.01367	+	1.75573i	0.122926	+	0.212913i
$69$	0.467911	−	0.810446i	0.0563299	−	0.0975662i
$70$	3.93242	−	1.43128i	0.470014	−	0.171071i
$71$	2.38919	+	13.5497i	0.283544	+	1.60806i	0.710440	+	0.703758i	$0.248496\pi$
$71$	2.38919	+	13.5497i	0.283544	+	1.60806i	−0.426896	+	0.904301i	$0.640393\pi$
$72$	−1.33868	+	7.59202i	−0.157765	+	0.894728i
$73$	7.06418	+	2.57115i	0.826799	+	0.300930i	0.720545	−	0.693409i	$-0.243892\pi$
$73$	7.06418	+	2.57115i	0.826799	+	0.300930i	0.106255	+	0.994339i	$0.466114\pi$
$74$	−0.564178	+	0.473401i	−0.0655843	+	0.0550318i
$75$	−0.751030			−0.0867214
$76$		0			0
$77$	−6.41147			−0.730655
$78$	1.89646	−	1.59132i	0.214732	−	0.180181i
$79$	−6.54323	−	2.38154i	−0.736171	−	0.267944i	−0.0533965	−	0.998573i	$-0.517005\pi$
$79$	−6.54323	−	2.38154i	−0.736171	−	0.267944i	−0.682775	+	0.730629i	$0.739227\pi$
$80$	0.0184183	−	0.104455i	0.00205923	−	0.0116785i
$81$	1.13429	+	6.43285i	0.126032	+	0.714761i
$82$	3.71048	−	1.35051i	0.409754	−	0.149138i
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	−0.926698	−	0.375807i	$-0.877366\pi$
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	0.788807	+	0.614641i	$0.210699\pi$
$84$	0.613341	+	1.06234i	0.0669210	+	0.115911i
$85$	−3.20574	−	2.68993i	−0.347711	−	0.291764i
$86$	−3.23396	−	2.71361i	−0.348726	−	0.292616i
$87$	0.922618	+	1.59802i	0.0989151	+	0.171326i
$88$	−4.84002	+	8.38316i	−0.515948	+	0.893648i
$89$	−2.14543	+	0.780873i	−0.227415	+	0.0827723i	−0.453214	−	0.891401i	$-0.649723\pi$
$89$	−2.14543	+	0.780873i	−0.227415	+	0.0827723i	0.225799	+	0.974174i	$0.427501\pi$
$90$	−1.05051	−	5.95772i	−0.110733	−	0.627999i
$91$	−1.72668	+	9.79250i	−0.181005	+	1.02653i
$92$	2.02734	+	0.737892i	0.211365	+	0.0769305i
$93$	0.792204	−	0.664738i	0.0821477	−	0.0689301i
$94$	−0.630415			−0.0650223
$95$		0			0
$96$	3.00000			0.306186
$97$	1.39646	−	1.17177i	0.141789	−	0.118975i	−0.569135	−	0.822244i	$-0.692722\pi$
$97$	1.39646	−	1.17177i	0.141789	−	0.118975i	0.710924	+	0.703269i	$0.248277\pi$
$98$	−2.86571	−	1.04303i	−0.289481	−	0.105362i
$99$	−1.60947	+	9.12776i	−0.161758	+	0.917374i
$100$	−0.300660	−	1.70513i	−0.0300660	−	0.170513i
$101$	7.44356	−	2.70924i	0.740662	−	0.269579i	0.0559912	−	0.998431i	$-0.482168\pi$
$101$	7.44356	−	2.70924i	0.740662	−	0.269579i	0.684671	+	0.728852i	$0.259946\pi$
$102$	−0.386659	+	0.669713i	−0.0382850	+	0.0663115i
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	0.865667	−	0.500621i	$-0.166895\pi$
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	−0.866384	+	0.499379i	$0.833561\pi$
$104$	11.5005	+	9.65004i	1.12771	+	0.946264i
$105$	−1.93969	−	1.62760i	−0.189295	−	0.158837i
$106$	2.68479	+	4.65020i	0.260770	+	0.451667i
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	−0.939052	−	0.343776i	$-0.888294\pi$
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	0.767244	+	0.641355i	$0.221627\pi$
$108$	3.50640	−	1.27622i	0.337403	−	0.122805i
$109$	−1.27972	−	7.25762i	−0.122574	−	0.695154i	−0.982719	−	0.185104i	$-0.940738\pi$
$109$	−1.27972	−	7.25762i	−0.122574	−	0.695154i	0.860144	−	0.510050i	$-0.170373\pi$
$110$	1.31908	−	7.48086i	0.125769	−	0.713272i
$111$	0.418748	+	0.152412i	0.0397458	+	0.0144663i
$112$	0.0603074	−	0.0506039i	0.00569851	−	0.00478162i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$		0			0
$115$	−4.45336			−0.415278
$116$	−3.25877	+	2.73443i	−0.302569	+	0.253886i
$117$	13.5077	+	4.91642i	1.24879	+	0.454523i
$118$	−1.64290	+	9.31737i	−0.151242	+	0.857733i
$119$	−0.539363	−	3.05888i	−0.0494433	−	0.280407i
$120$	−3.59240	+	1.30753i	−0.327939	+	0.119360i
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	1.92989	+	3.34267i	0.174724	+	0.302631i
$123$	−1.83022	−	1.53574i	−0.165026	−	0.138473i
$124$	1.82635	+	1.53249i	0.164011	+	0.137622i
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$	2.24510	−	3.88863i	0.200009	−	0.346426i
$127$	−0.0949225	+	0.0345490i	−0.00842301	+	0.00306572i	−0.346228	−	0.938150i	$-0.612538\pi$
$127$	−0.0949225	+	0.0345490i	−0.00842301	+	0.00306572i	0.337805	+	0.941216i	$0.390315\pi$
$128$	1.18820	+	6.73859i	0.105023	+	0.595613i
$129$	−0.443563	+	2.51557i	−0.0390535	+	0.221484i
$130$	−11.0706	−	4.02936i	−0.970954	−	0.353398i
$131$	−2.32635	+	1.95204i	−0.203254	+	0.170551i	−0.738733	−	0.673998i	$-0.764576\pi$
$131$	−2.32635	+	1.95204i	−0.203254	+	0.170551i	0.535479	+	0.844549i	$0.320131\pi$
$132$	2.22668			0.193808
$133$		0			0
$134$	12.4979			1.07966
$135$	−5.90033	+	4.95096i	−0.507820	+	0.426111i
$136$	−4.40673	−	1.60392i	−0.377874	−	0.137535i
$137$	3.39306	−	19.2430i	0.289888	−	1.64404i	−0.397394	−	0.917648i	$-0.630085\pi$
$137$	3.39306	−	19.2430i	0.289888	−	1.64404i	0.687282	−	0.726390i	$-0.258803\pi$
$138$	0.142903	+	0.810446i	0.0121648	+	0.0689897i
$139$	−14.4684	+	5.26606i	−1.22719	+	0.446661i	−0.872635	−	0.488373i	$-0.837591\pi$
$139$	−14.4684	+	5.26606i	−1.22719	+	0.446661i	−0.354557	+	0.935034i	$0.615368\pi$
$140$	2.91875	−	5.05542i	0.246679	−	0.427261i
$141$	0.190722	+	0.330341i	0.0160617	+	0.0278197i
$142$	−9.26857	−	7.77725i	−0.777801	−	0.652653i
$143$	13.8268	+	11.6021i	1.15626	+	0.970215i
$144$	−0.0569038	−	0.0985603i	−0.00474198	−	0.00821336i
$145$	4.39053	−	7.60462i	0.364614	−	0.631529i
$146$	−6.21213	+	2.26103i	−0.514120	+	0.187124i
$147$	0.320422	+	1.81720i	0.0264280	+	0.149880i
$148$	−0.178396	+	1.01173i	−0.0146641	+	0.0831640i
$149$	3.53936	+	1.28822i	0.289956	+	0.105535i	0.482903	−	0.875674i	$-0.339582\pi$
$149$	3.53936	+	1.28822i	0.289956	+	0.105535i	−0.192947	+	0.981209i	$0.561805\pi$
$150$	0.505930	−	0.424525i	0.0413090	−	0.0346624i
$151$	14.5963			1.18783			0.593914	−	0.804529i	$-0.297582\pi$
$151$	14.5963			1.18783			0.593914	+	0.804529i	$0.297582\pi$
$152$		0			0
$153$	−4.49020			−0.363011
$154$	4.31908	−	3.62414i	0.348041	−	0.292041i
$155$	−4.62449	−	1.68317i	−0.371448	−	0.135196i
$156$	0.599670	−	3.40090i	0.0480120	−	0.272290i
$157$	−1.80154	−	10.2170i	−0.143778	−	0.815407i	−0.968340	−	0.249635i	$-0.919689\pi$
$157$	−1.80154	−	10.2170i	−0.143778	−	0.815407i	0.824562	−	0.565772i	$-0.191422\pi$
$158$	5.75402	−	2.09429i	0.457765	−	0.166613i
$159$	1.62449	−	2.81369i	0.128830	−	0.223140i
$160$	−7.13816	−	12.3636i	−0.564321	−	0.977432i
$161$	−2.53209	−	2.12467i	−0.199557	−	0.167448i
$162$	−4.40033	−	3.69232i	−0.345723	−	0.290096i
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	0.902905	−	0.429841i	$-0.141430\pi$
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	−0.823706	+	0.567018i	$0.808097\pi$
$164$	2.75402	−	4.77011i	0.215053	−	0.372483i
$165$	−4.31908	+	1.57202i	−0.336240	+	0.122381i
$166$	−0.383666	−	2.17588i	−0.0297783	−	0.168881i
$167$	4.03849	−	22.9034i	0.312507	−	1.77232i	−0.273361	−	0.961911i	$-0.588135\pi$
$167$	4.03849	−	22.9034i	0.312507	−	1.77232i	0.585869	−	0.810406i	$-0.300753\pi$
$168$	−2.66637	−	0.970481i	−0.205715	−	0.0748742i
$169$	11.4855	−	9.63744i	0.883496	−	0.741341i
$170$	3.68004			0.282247
$171$		0			0
$172$	−5.88888			−0.449023
$173$	−0.686852	+	0.576337i	−0.0522204	+	0.0438181i	−0.668524	−	0.743690i	$-0.733074\pi$
$173$	−0.686852	+	0.576337i	−0.0522204	+	0.0438181i	0.616304	+	0.787508i	$0.288629\pi$
$174$	−1.52481	−	0.554987i	−0.115596	−	0.0420735i
$175$	−0.460637	+	2.61240i	−0.0348209	+	0.197479i
$176$	−0.0248149	−	0.140732i	−0.00187050	−	0.0106081i
$177$	5.37939	−	1.95794i	0.404339	−	0.147167i
$178$	1.00387	−	1.73875i	0.0752433	−	0.130325i
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	−0.921755	−	0.387773i	$-0.873245\pi$
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	0.125056	−	0.992150i	$-0.460089\pi$
$180$	−6.46451	−	5.42437i	−0.481836	−	0.404308i
$181$	12.3327	+	10.3484i	0.916686	+	0.769191i	0.973379	−	0.229201i	$-0.0736112\pi$
$181$	12.3327	+	10.3484i	0.916686	+	0.769191i	−0.0566932	+	0.998392i	$0.518056\pi$
$182$	−4.37211	−	7.57272i	−0.324082	−	0.561327i
$183$	1.16772	−	2.02255i	0.0863202	−	0.149511i
$184$	−4.68954	+	1.70685i	−0.345717	+	0.125831i
$185$	−0.368241	−	2.08840i	−0.0270736	−	0.153542i
$186$	−0.157918	+	0.895599i	−0.0115791	+	0.0656685i
$187$	−5.29813	−	1.92836i	−0.387438	−	0.141016i
$188$	−0.673648	+	0.565258i	−0.0491308	+	0.0412257i
$189$	−5.71688			−0.415842
$190$		0			0
$191$	18.9486			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$192$	−2.05509	+	1.72443i	−0.148314	+	0.124450i
$193$	12.1236	+	4.41263i	0.872676	+	0.317628i	0.739250	−	0.673431i	$-0.235180\pi$
$193$	12.1236	+	4.41263i	0.872676	+	0.317628i	0.133426	+	0.991059i	$0.457402\pi$
$194$	−0.278371	+	1.57872i	−0.0199859	+	0.113345i
$195$	1.23783	+	7.02006i	0.0886426	+	0.502717i
$196$	−3.99747	+	1.45496i	−0.285534	+	0.103926i
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	−0.0743108	−	0.997235i	$-0.523676\pi$
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	0.900786	−	0.434263i	$-0.142991\pi$
$198$	−4.07532	−	7.05866i	−0.289621	−	0.501637i
$199$	7.06418	+	5.92755i	0.500766	+	0.420193i	0.857866	−	0.513873i	$-0.171790\pi$
$199$	7.06418	+	5.92755i	0.500766	+	0.420193i	−0.357100	+	0.934066i	$0.616234\pi$
$200$	3.06805	+	2.57440i	0.216944	+	0.182037i
$201$	−3.78106	−	6.54899i	−0.266695	−	0.461930i
$202$	−3.48293	+	6.03260i	−0.245058	+	0.424453i
$203$	6.12449	−	2.22913i	0.429855	−	0.156454i
$204$	0.187319	+	1.06234i	0.0131149	+	0.0743785i
$205$	−1.97431	+	11.1969i	−0.137892	+	0.782022i
$206$	0.0120217	+	0.00437554i	0.000837592	+	0.000304858i
$207$	−3.66044	+	3.07148i	−0.254418	+	0.213482i
$208$	−0.221629			−0.0153672
$209$		0			0
$210$	2.22668			0.153656
$211$	−11.2023	+	9.39987i	−0.771200	+	0.647114i	−0.941016	−	0.338362i	$-0.890127\pi$
$211$	−11.2023	+	9.39987i	−0.771200	+	0.647114i	0.169816	+	0.985476i	$0.445683\pi$
$212$	7.03849	+	2.56180i	0.483405	+	0.175945i
$213$	−1.27126	+	7.20967i	−0.0871052	+	0.493998i
$214$	−0.542766	−	3.07818i	−0.0371027	−	0.210420i
$215$	11.4226	−	4.15749i	0.779016	−	0.283539i
$216$	−4.31567	+	7.47497i	−0.293644	+	0.508607i
$217$	−1.82635	−	3.16333i	−0.123981	−	0.214741i
$218$	4.96451	+	4.16572i	0.336239	+	0.282138i
$219$	3.06418	+	2.57115i	0.207058	+	0.173742i
$220$	−5.29813	−	9.17664i	−0.357200	−	0.618689i
$221$	−4.37211	+	7.57272i	−0.294100	+	0.509396i
$222$	−0.368241	+	0.134029i	−0.0247147	+	0.00899542i
$223$	0.523471	+	2.96875i	0.0350542	+	0.198802i	0.997306	−	0.0733603i	$-0.0233723\pi$
$223$	0.523471	+	2.96875i	0.0350542	+	0.198802i	−0.962251	+	0.272162i	$0.912261\pi$
$224$	1.84002	−	10.4353i	0.122942	−	0.697237i
$225$	3.60354	+	1.31158i	0.240236	+	0.0874388i
$226$	4.96972	−	4.17009i	0.330581	−	0.277390i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	3.00000	−	2.51730i	0.197814	−	0.165986i
$231$	−3.20574	−	1.16679i	−0.210922	−	0.0767693i
$232$	1.70873	−	9.69069i	0.112184	−	0.636225i
$233$	−4.19981	−	23.8183i	−0.275139	−	1.56039i	−0.738521	−	0.674230i	$-0.764476\pi$
$233$	−4.19981	−	23.8183i	−0.275139	−	1.56039i	0.463383	−	0.886158i	$-0.346635\pi$
$234$	−11.8785	+	4.32342i	−0.776522	+	0.282631i
$235$	0.907604	−	1.57202i	0.0592055	−	0.102547i
$236$	6.59879	+	11.4294i	0.429545	+	0.743993i
$237$	−2.83821	−	2.38154i	−0.184362	−	0.154698i
$238$	2.09240	+	1.75573i	0.135630	+	0.113807i
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	0.945665	+	0.325143i	$0.105413\pi$
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	−0.191250	+	0.981541i	$0.561254\pi$
$240$	0.0282185	−	0.0488759i	0.00182150	−	0.00315492i
$241$	0.279715	−	0.101808i	0.0180180	−	0.00655803i	−0.332995	−	0.942928i	$-0.608059\pi$
$241$	0.279715	−	0.101808i	0.0180180	−	0.00655803i	0.351013	+	0.936370i	$0.385837\pi$
$242$	−0.0974487	−	0.552659i	−0.00626424	−	0.0355263i
$243$	−2.18820	+	12.4099i	−0.140373	+	0.796094i
$244$	5.05943	+	1.84148i	0.323897	+	0.117889i
$245$	6.72668	−	5.64436i	0.429752	−	0.360605i
$246$	2.10101			0.133956
$247$		0			0
$248$	−5.51485			−0.350193
$249$	−1.02410	+	0.859322i	−0.0648997	+	0.0544573i
$250$	7.50862	+	2.73291i	0.474887	+	0.172845i
$251$	−2.81268	+	15.9515i	−0.177535	+	1.00685i	0.757642	+	0.652670i	$0.226351\pi$
$251$	−2.81268	+	15.9515i	−0.177535	+	1.00685i	−0.935177	+	0.354180i	$0.884760\pi$
$252$	−1.08765	−	6.16836i	−0.0685154	−	0.388570i
$253$	−5.63816	+	2.05212i	−0.354468	+	0.129016i
$254$	0.0444153	−	0.0769295i	0.00278686	−	0.00482699i
$255$	−1.11334	−	1.92836i	−0.0697201	−	0.120759i
$256$	−12.3341	−	10.3495i	−0.770881	−	0.646846i
$257$	−11.7626	−	9.87003i	−0.733733	−	0.615675i	0.197413	−	0.980320i	$-0.436746\pi$
$257$	−11.7626	−	9.87003i	−0.733733	−	0.615675i	−0.931147	+	0.364645i	$0.881190\pi$
$258$	−1.12314	−	1.94534i	−0.0699237	−	0.121111i
$259$	0.786989	−	1.36310i	0.0489011	−	0.0846992i
$260$	−15.4427	+	5.62068i	−0.957715	+	0.348580i
$261$	−1.63610	−	9.27876i	−0.101272	−	0.574341i
$262$	0.463736	−	2.62998i	0.0286497	−	0.162481i
$263$	−9.06165	−	3.29817i	−0.558765	−	0.203374i	0.0471713	−	0.998887i	$-0.484979\pi$
$263$	−9.06165	−	3.29817i	−0.558765	−	0.203374i	−0.605937	+	0.795513i	$0.707202\pi$
$264$	−3.94562	+	3.31077i	−0.242836	+	0.203764i
$265$	−15.4611			−0.949768
$266$		0			0
$267$	−1.21482			−0.0743459
$268$	13.3550	−	11.2062i	0.815789	−	0.684528i
$269$	−17.1766	−	6.25179i	−1.04728	−	0.381178i	−0.239643	−	0.970861i	$-0.577031\pi$
$269$	−17.1766	−	6.25179i	−1.04728	−	0.381178i	−0.807635	+	0.589683i	$0.799253\pi$
$270$	1.17617	−	6.67042i	0.0715797	−	0.405949i
$271$	3.29308	+	18.6760i	0.200040	+	1.13449i	0.905056	+	0.425293i	$0.139829\pi$
$271$	3.29308	+	18.6760i	0.200040	+	1.13449i	−0.705015	+	0.709192i	$0.749060\pi$
$272$	0.0650551	−	0.0236781i	0.00394455	−	0.00143570i
$273$	−2.64543	+	4.58202i	−0.160109	+	0.277316i
$274$	8.59152	+	14.8809i	0.519033	+	0.898991i
$275$	3.68866	+	3.09516i	0.222435	+	0.186645i
$276$	0.879385	+	0.737892i	0.0529328	+	0.0444159i
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	0.581775	−	0.813350i	$-0.302358\pi$
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	−0.995269	+	0.0971571i	$0.969025\pi$
$278$	6.76991	−	11.7258i	0.406033	−	0.703269i
$279$	−4.96198	+	1.80601i	−0.297066	+	0.108123i
$280$	2.34477	+	13.2979i	0.140127	+	0.794699i
$281$	−2.27672	+	12.9119i	−0.135818	+	0.770261i	0.838469	+	0.544949i	$0.183451\pi$
$281$	−2.27672	+	12.9119i	−0.135818	+	0.770261i	−0.974287	+	0.225312i	$0.927660\pi$
$282$	−0.315207	−	0.114726i	−0.0187703	−	0.00683184i
$283$	−13.3118	+	11.1699i	−0.791305	+	0.663983i	−0.946068	−	0.323968i	$-0.894983\pi$
$283$	−13.3118	+	11.1699i	−0.791305	+	0.663983i	0.154763	+	0.987952i	$0.450538\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	−6.46451	+	5.42437i	−0.381588	+	0.320190i
$288$	−14.3944	−	5.23913i	−0.848198	−	0.308719i
$289$	−2.47771	+	14.0518i	−0.145748	+	0.826576i
$290$	1.34090	+	7.60462i	0.0787403	+	0.446559i
$291$	0.911474	−	0.331749i	0.0534316	−	0.0194475i
$292$	−4.61081	+	7.98617i	−0.269828	+	0.467355i
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	0.998734	−	0.0503091i	$-0.0160206\pi$
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	−0.542936	+	0.839774i	$0.682687\pi$
$294$	−1.24304	−	1.04303i	−0.0724956	−	0.0608310i
$295$	−20.8687	−	17.5109i	−1.21502	−	1.01953i
$296$	−1.18820	−	2.05802i	−0.0690625	−	0.119620i
$297$	−5.18866	+	8.98703i	−0.301077	+	0.521480i
$298$	−3.11246	+	1.13284i	−0.180300	+	0.0656239i
$299$	1.61587	+	9.16404i	0.0934480	+	0.529970i
$300$	0.159978	−	0.907278i	0.00923631	−	0.0523817i
$301$	8.47818	+	3.08580i	0.488674	+	0.177863i
$302$	−9.83275	+	8.25066i	−0.565811	+	0.474772i
$303$	4.21482			0.242135
$304$		0			0
$305$	−11.1138			−0.636375
$306$	3.02481	−	2.53812i	0.172917	−	0.145095i
$307$	20.2224	+	7.36035i	1.15415	+	0.420077i	0.847005	−	0.531584i	$-0.178403\pi$
$307$	20.2224	+	7.36035i	1.15415	+	0.420077i	0.307148	+	0.951662i	$0.400625\pi$
$308$	1.36571	−	7.74535i	0.0778188	−	0.441332i
$309$	−0.00134417	−	0.00762319i	−7.64674e−5	−	0.000433668i
$310$	4.06670	−	1.48016i	0.230973	−	0.0840674i
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	−0.994997	−	0.0999083i	$-0.968145\pi$
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	0.584021	+	0.811738i	$0.301478\pi$
$312$	3.99407	+	6.91793i	0.226120	+	0.391651i
$313$	14.9520	+	12.5462i	0.845138	+	0.709155i	0.958713	−	0.284374i	$-0.0917859\pi$
$313$	14.9520	+	12.5462i	0.845138	+	0.709155i	−0.113575	+	0.993529i	$0.536230\pi$
$314$	6.98886	+	5.86435i	0.394404	+	0.330944i
$315$	6.46451	+	11.1969i	0.364234	+	0.630871i
$316$	4.27079	−	7.39723i	0.240251	−	0.416127i
$317$	26.6377	−	9.69535i	1.49612	−	0.544545i	0.541071	−	0.840977i	$-0.318019\pi$
$317$	26.6377	−	9.69535i	1.49612	−	0.544545i	0.955054	+	0.296432i	$0.0957968\pi$
$318$	0.496130	+	2.81369i	0.0278216	+	0.157784i
$319$	2.05438	−	11.6510i	0.115023	−	0.652328i
$320$	11.9966	+	4.36640i	0.670630	+	0.244089i
$321$	−1.44878	+	1.21567i	−0.0808629	+	0.0678520i
$322$	2.90673			0.161986
$323$		0			0
$324$	−8.01279			−0.445155
$325$	5.72075	−	4.80028i	0.317330	−	0.266272i
$326$	−1.67112	−	0.608239i	−0.0925549	−	0.0336872i
$327$	0.680922	−	3.86170i	0.0376551	−	0.213553i
$328$	2.21244	+	12.5474i	0.122161	+	0.692812i
$329$	1.26604	−	0.460802i	0.0697993	−	0.0254049i
$330$	2.02094	−	3.50038i	0.111249	−	0.192690i
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	0.841570	−	0.540148i	$-0.181632\pi$
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	−0.888567	+	0.458747i	$0.848298\pi$
$332$	−2.36097	−	1.98109i	−0.129575	−	0.108726i
$333$	−1.74304	−	1.46258i	−0.0955180	−	0.0801491i
$334$	10.2258	+	17.7116i	0.559531	+	0.969136i
$335$	−17.9932	+	31.1651i	−0.983073	+	1.70273i
$336$	0.0393628	−	0.0143269i	0.00214742	−	0.000781597i
$337$	−4.41740	−	25.0523i	−0.240631	−	1.36469i	−0.830423	−	0.557133i	$-0.811901\pi$
$337$	−4.41740	−	25.0523i	−0.240631	−	1.36469i	0.589792	−	0.807555i	$-0.299210\pi$
$338$	−2.28952	+	12.9845i	−0.124533	+	0.706263i
$339$	−3.68866	−	1.34256i	−0.200341	−	0.0729180i
$340$	3.93242	−	3.29969i	0.213265	−	0.178951i
$341$	−6.63041			−0.359057
$342$		0			0
$343$	19.6732			1.06225
$344$	10.4349	−	8.75596i	0.562615	−	0.472090i
$345$	−2.22668	−	0.810446i	−0.119881	−	0.0436329i
$346$	0.136917	−	0.776497i	0.00736072	−	0.0417447i
$347$	1.33750	+	7.58532i	0.0718006	+	0.407201i	0.999432	+	0.0337040i	$0.0107303\pi$
$347$	1.33750	+	7.58532i	0.0718006	+	0.407201i	−0.927631	+	0.373497i	$0.878159\pi$
$348$	−2.12701	+	0.774169i	−0.114020	+	0.0414998i
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	0.382315	+	0.924032i	$0.375127\pi$
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	−0.991393	+	0.130921i	$0.958206\pi$
$350$	−1.16637	−	2.02022i	−0.0623453	−	0.107985i
$351$	12.3289	+	10.3452i	0.658067	+	0.552184i
$352$	−14.7344	−	12.3636i	−0.785347	−	0.658985i
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	0.977171	−	0.212454i	$-0.0681457\pi$
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	−0.672576	+	0.740028i	$0.734812\pi$
$354$	−2.51707	+	4.35970i	−0.133781	+	0.231715i
$355$	32.7374	−	11.9154i	1.73752	−	0.632406i
$356$	−0.486329	−	2.75811i	−0.0257754	−	0.146180i
$357$	0.286989	−	1.62760i	0.0151891	−	0.0861415i
$358$	17.6163	+	6.41182i	0.931052	+	0.338875i
$359$	7.95471	−	6.67479i	0.419833	−	0.352282i	−0.408266	−	0.912863i	$-0.633867\pi$
$359$	7.95471	−	6.67479i	0.419833	−	0.352282i	0.828100	+	0.560581i	$0.189422\pi$
$360$	19.5202			1.02881
$361$		0			0
$362$	−14.1575			−0.744099
$363$	−0.260115	+	0.218262i	−0.0136525	+	0.0114558i
$364$	−11.4620	−	4.17182i	−0.600771	−	0.218663i
$365$	3.30541	−	18.7459i	0.173013	−	0.981205i
$366$	0.356630	+	2.02255i	0.0186413	+	0.105720i
$367$	30.5710	−	11.1269i	1.59580	−	0.580822i	0.617234	−	0.786779i	$-0.288253\pi$
$367$	30.5710	−	11.1269i	1.59580	−	0.580822i	0.978561	+	0.205957i	$0.0660308\pi$
$368$	0.0368366	−	0.0638029i	0.00192024	−	0.00332596i
$369$	6.09967	+	10.5649i	0.317536	+	0.549989i
$370$	1.42855	+	1.19869i	0.0742667	+	0.0623172i
$371$	−8.79086	−	7.37641i	−0.456399	−	0.382964i
$372$	0.634285	+	1.09861i	0.0328862	+	0.0569605i
$373$	15.2429	−	26.4014i	0.789246	−	1.36701i	−0.137183	−	0.990546i	$-0.543805\pi$
$373$	15.2429	−	26.4014i	0.789246	−	1.36701i	0.926429	−	0.376469i	$-0.122862\pi$
$374$	4.65910	−	1.69577i	0.240916	−	0.0876864i
$375$	−0.839556	−	4.76136i	−0.0433545	−	0.245875i
$376$	0.353226	−	2.00324i	0.0182162	−	0.103309i
$377$	−17.2417	−	6.27546i	−0.887993	−	0.323203i
$378$	3.85117	−	3.23151i	0.198083	−	0.166211i
$379$	−17.8598			−0.917396			−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598			−0.917396			−0.458698	+	0.888592i	$0.651684\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$	−12.7647	+	10.7109i	−0.653099	+	0.548015i
$383$	−22.0415	−	8.02244i	−1.12627	−	0.409928i	−0.289331	−	0.957229i	$-0.593433\pi$
$383$	−22.0415	−	8.02244i	−1.12627	−	0.409928i	−0.836936	+	0.547301i	$0.815655\pi$
$384$	−0.632226	+	3.58553i	−0.0322631	+	0.182973i
$385$	2.81908	+	15.9878i	0.143674	+	0.814813i
$386$	−10.6613	+	3.88040i	−0.542647	+	0.197507i
$387$	6.52141	−	11.2954i	0.331502	−	0.574178i
$388$	1.11809	+	1.93659i	0.0567623	+	0.0983153i
$389$	2.99479	+	2.51292i	0.151842	+	0.127410i	0.715544	−	0.698568i	$-0.246179\pi$
$389$	2.99479	+	2.51292i	0.151842	+	0.127410i	−0.563702	+	0.825978i	$0.690623\pi$
$390$	−4.80200	−	4.02936i	−0.243159	−	0.204035i
$391$	−1.45336	−	2.51730i	−0.0734997	−	0.127305i
$392$	4.92009	−	8.52185i	0.248502	−	0.430418i
$393$	−1.51842	+	0.552659i	−0.0765941	+	0.0278780i
$394$	3.54277	+	20.0920i	0.178482	+	1.01222i
$395$	−3.06165	+	17.3635i	−0.154048	+	0.873652i
$396$	−10.6839	−	3.88863i	−0.536887	−	0.195411i
$397$	6.86303	−	5.75876i	0.344445	−	0.289024i	−0.454110	−	0.890946i	$-0.650043\pi$
$397$	6.86303	−	5.75876i	0.344445	−	0.289024i	0.798555	+	0.601922i	$0.205598\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	1.55303	−	1.30315i	0.0775548	−	0.0650762i	−0.603186	−	0.797600i	$-0.706102\pi$
$401$	1.55303	−	1.30315i	0.0775548	−	0.0650762i	0.680741	+	0.732524i	$0.261658\pi$
$402$	6.24897	+	2.27444i	0.311670	+	0.113439i
$403$	−1.78564	+	10.1269i	−0.0889493	+	0.504457i
$404$	1.68732	+	9.56926i	0.0839472	+	0.476088i
$405$	15.5424	−	5.65695i	0.772306	−	0.281096i
$406$	−2.86571	+	4.96356i	−0.142223	+	0.246338i
$407$	−1.42855	−	2.47432i	−0.0708105	−	0.122647i
$408$	−1.91147	−	1.60392i	−0.0946321	−	0.0794057i
$409$	24.6728	+	20.7029i	1.21999	+	1.02369i	0.998825	+	0.0484567i	$0.0154303\pi$
$409$	24.6728	+	20.7029i	1.21999	+	1.02369i	0.221165	+	0.975236i	$0.429014\pi$
$410$	−4.99912	−	8.65873i	−0.246889	−	0.427624i
$411$	5.19846	−	9.00400i	0.256421	−	0.444135i
$412$	0.0167694	−	0.00610358i	0.000826171	−	0.000300702i
$413$	−3.51114	−	19.9127i	−0.172772	−	0.979839i
$414$	0.729675	−	4.13819i	0.0358616	−	0.203381i
$415$	5.97818	+	2.17588i	0.293457	+	0.106810i
$416$	−22.8516	+	19.1748i	−1.12039	+	0.940122i
$417$	−8.19253			−0.401190
$418$		0			0
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$	2.37939	−	1.99654i	0.116102	−	0.0974212i
$421$	6.06418	+	2.20718i	0.295550	+	0.107571i	0.485540	−	0.874215i	$-0.338623\pi$
$421$	6.06418	+	2.20718i	0.295550	+	0.107571i	−0.189990	+	0.981786i	$0.560845\pi$
$422$	2.23308	−	12.6644i	0.108705	−	0.616494i
$423$	−0.338211	−	1.91809i	−0.0164444	−	0.0932608i
$424$	−16.2811	+	5.92582i	−0.790678	+	0.287783i
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$	−3.21894	−	5.57537i	−0.155958	−	0.270128i
$427$	−6.31908	−	5.30234i	−0.305802	−	0.256598i
$428$	−3.34002	−	2.80261i	−0.161446	−	0.135469i
$429$	4.80200	+	8.31731i	0.231843	+	0.401564i
$430$	−5.34477	+	9.25741i	−0.257748	+	0.446432i
$431$	−13.1532	+	4.78736i	−0.633566	+	0.230599i	−0.638783	−	0.769387i	$-0.720562\pi$
$431$	−13.1532	+	4.78736i	−0.633566	+	0.230599i	0.00521671	+	0.999986i	$0.498339\pi$
$432$	−0.0221266	−	0.125486i	−0.00106457	−	0.00603745i
$433$	4.98246	−	28.2569i	0.239442	−	1.35794i	−0.593613	−	0.804751i	$-0.702299\pi$
$433$	4.98246	−	28.2569i	0.239442	−	1.35794i	0.833055	−	0.553191i	$-0.186590\pi$
$434$	3.01842	+	1.09861i	0.144889	+	0.0527352i
$435$	3.57919	−	3.00330i	0.171609	−	0.143997i
$436$	9.04013			0.432944
$437$		0			0
$438$	−3.51754			−0.168075
$439$	10.2208	−	8.57623i	0.487810	−	0.409321i	−0.365431	−	0.930839i	$-0.619078\pi$
$439$	10.2208	−	8.57623i	0.487810	−	0.409321i	0.853241	+	0.521517i	$0.174634\pi$
$440$	23.0326	+	8.38316i	1.09803	+	0.399652i
$441$	1.63610	−	9.27876i	0.0779093	−	0.441846i
$442$	−1.33527	−	7.57272i	−0.0635125	−	0.360198i
$443$	−31.8396	+	11.5887i	−1.51275	+	0.550594i	−0.959324	−	0.282307i	$-0.908900\pi$
$443$	−31.8396	+	11.5887i	−1.51275	+	0.550594i	−0.553421	+	0.832901i	$0.686678\pi$
$444$	−0.273318	+	0.473401i	−0.0129711	+	0.0224666i
$445$	2.89053	+	5.00654i	0.137024	+	0.237333i
$446$	−2.03074	−	1.70400i	−0.0961585	−	0.0806866i
$447$	1.53524	+	1.28822i	0.0726146	+	0.0609308i
$448$	4.73783	+	8.20616i	0.223841	+	0.387704i
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	−0.553460	−	0.832876i	$-0.686693\pi$
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	0.998022	+	0.0628725i	$0.0200261\pi$
$450$	−3.16890	+	1.15339i	−0.149383	+	0.0543711i
$451$	2.65998	+	15.0855i	0.125253	+	0.710348i
$452$	1.57145	−	8.91215i	0.0739149	−	0.419192i
$453$	7.29813	+	2.65630i	0.342896	+	0.124804i
$454$	−9.24376	+	7.75643i	−0.433831	+	0.364027i
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	−6.34183	+	5.32143i	−0.296334	+	0.248654i
$459$	−4.72416	−	1.71945i	−0.220505	−	0.0802571i
$460$	0.948615	−	5.37987i	0.0442294	−	0.250838i
$461$	−2.41859	−	13.7165i	−0.112645	−	0.638840i	−0.987889	−	0.155160i	$-0.950411\pi$
$461$	−2.41859	−	13.7165i	−0.112645	−	0.638840i	0.875245	−	0.483681i	$-0.160700\pi$
$462$	2.81908	−	1.02606i	0.131155	−	0.0477367i
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	−0.844816	−	0.535056i	$-0.820290\pi$
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	0.885781	+	0.464104i	$0.153624\pi$
$464$	0.0726338	+	0.125805i	0.00337194	+	0.00584037i
$465$	−2.00593	−	1.68317i	−0.0930228	−	0.0780554i
$466$	16.2927	+	13.6712i	0.754743	+	0.633305i
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	−0.999933	−	0.0115724i	$-0.996316\pi$
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	0.489945	−	0.871754i	$-0.337017\pi$
$468$	−8.81655	+	15.2707i	−0.407545	+	0.705889i
$469$	−25.0993	+	9.13538i	−1.15898	+	0.421833i
$470$	0.277189	+	1.57202i	0.0127858	+	0.0725117i
$471$	0.958578	−	5.43636i	0.0441689	−	0.250494i
$472$	−28.6869	−	10.4412i	−1.32042	−	0.480594i
$473$	12.5458	−	10.5271i	0.576855	−	0.484039i
$474$	3.25814			0.149651
$475$		0			0
$476$	3.81016			0.174638
$477$	−12.7083	+	10.6635i	−0.581871	+	0.488248i
$478$	−19.2754	−	7.01568i	−0.881638	−	0.320890i
$479$	−4.42056	+	25.0702i	−0.201981	+	1.14549i	0.700140	+	0.714005i	$0.253121\pi$
$479$	−4.42056	+	25.0702i	−0.201981	+	1.14549i	−0.902121	+	0.431483i	$0.857990\pi$
$480$	−1.31908	−	7.48086i	−0.0602074	−	0.341453i
$481$	−4.16385	+	1.51552i	−0.189855	+	0.0691016i
$482$	−0.130882	+	0.226694i	−0.00596150	+	0.0103256i
$483$	−0.879385	−	1.52314i	−0.0400134	−	0.0693053i
$484$	−0.599670	−	0.503183i	−0.0272577	−	0.0228720i
$485$	−3.53596	−	2.96702i	−0.160560	−	0.134726i
$486$	−5.54071	−	9.59679i	−0.251332	−	0.435319i
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	0.489903	+	0.871777i	$0.337032\pi$
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	−0.999932	+	0.0116199i	$0.996301\pi$
$488$	−11.7032	+	4.25962i	−0.529779	+	0.192824i
$489$	0.186852	+	1.05969i	0.00844974	+	0.0479208i
$490$	−1.34090	+	7.60462i	−0.0605757	+	0.343542i
$491$	−14.6912	−	5.34716i	−0.663004	−	0.241314i	−0.0114713	−	0.999934i	$-0.503651\pi$
$491$	−14.6912	−	5.34716i	−0.663004	−	0.241314i	−0.651533	+	0.758620i	$0.725874\pi$
$492$	2.24510	−	1.88386i	0.101217	−	0.0849311i
$493$	5.73143			0.258131
$494$		0			0
$495$	23.4688			1.05485
$496$	0.0623668	−	0.0523319i	0.00280035	−	0.00234977i
$497$	24.2986	+	8.84397i	1.08994	+	0.396706i
$498$	0.204144	−	1.15776i	0.00914793	−	0.0518805i
$499$	−4.96926	−	28.1820i	−0.222454	−	1.26160i	−0.867492	−	0.497451i	$-0.834269\pi$
$499$	−4.96926	−	28.1820i	−0.222454	−	1.26160i	0.645038	−	0.764151i	$-0.276842\pi$
$500$	10.4740	−	3.81223i	0.468412	−	0.170488i
$501$	6.18732	−	10.7168i	0.276429	−	0.478789i
$502$	−7.12196	−	12.3356i	−0.317869	−	0.550565i
$503$	−19.1860	−	16.0989i	−0.855460	−	0.717816i	0.105525	−	0.994417i	$-0.466348\pi$
$503$	−19.1860	−	16.0989i	−0.855460	−	0.717816i	−0.960985	+	0.276600i	$0.910792\pi$
$504$	11.0988	+	9.31299i	0.494380	+	0.414834i
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$	2.63816	−	4.56942i	0.117280	−	0.203135i
$507$	7.49660	−	2.72854i	0.332936	−	0.121179i
$508$	−0.0215172	−	0.122030i	−0.000954671	−	0.00541421i
$509$	−5.82089	+	33.0119i	−0.258006	+	1.46323i	0.530230	+	0.847854i	$0.322106\pi$
$509$	−5.82089	+	33.0119i	−0.258006	+	1.46323i	−0.788236	+	0.615373i	$0.789005\pi$
$510$	1.84002	+	0.669713i	0.0814776	+	0.0296554i
$511$	10.8229	−	9.08153i	0.478779	−	0.401743i
$512$	0.473897			0.0209435
$513$		0			0
$514$	13.5030			0.595591
$515$	−0.0282185	+	0.0236781i	−0.00124346	+	0.00104338i
$516$	−2.94444	−	1.07169i	−0.129622	−	0.0471785i
$517$	0.424678	−	2.40847i	0.0186773	−	0.105924i
$518$	0.240352	+	1.36310i	0.0105605	+	0.0598914i
$519$	−0.448311	+	0.163172i	−0.0196787	+	0.00716245i
$520$	19.0069	−	32.9209i	0.833506	−	1.44367i
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	−0.992530	−	0.122005i	$-0.961068\pi$
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	0.390606	−	0.920558i	$-0.372266\pi$
$522$	6.34705	+	5.32581i	0.277803	+	0.233104i
$523$	7.93423	+	6.65761i	0.346940	+	0.291117i	0.799560	−	0.600587i	$-0.205066\pi$
$523$	7.93423	+	6.65761i	0.346940	+	0.291117i	−0.452620	+	0.891703i	$0.649511\pi$
$524$	−1.86262	−	3.22615i	−0.0813687	−	0.140935i
$525$	−0.705737	+	1.22237i	−0.0308009	+	0.0533487i
$526$	7.96868	−	2.90036i	0.347451	−	0.126462i
$527$	−0.557781	−	3.16333i	−0.0242973	−	0.137797i
$528$	0.0132037	−	0.0748822i	0.000574619	−	0.00325883i
$529$	18.7062	+	6.80850i	0.813313	+	0.296022i
$530$	10.4153	−	8.73951i	0.452414	−	0.379620i
$531$	−29.2303			−1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$	0.818363	−	0.686688i	0.0354140	−	0.0297159i
$535$	8.45723	+	3.07818i	0.365638	+	0.133081i
$536$	−7.00269	+	39.7142i	−0.302470	+	1.71539i
$537$	−1.96972	−	11.1708i	−0.0849998	−	0.482058i
$538$	15.1049	−	5.49773i	0.651218	−	0.237024i
$539$	5.91534	−	10.2457i	0.254792	−	0.441313i
$540$	−4.72416	−	8.18248i	−0.203295	−	0.352118i
$541$	1.93376	+	1.62262i	0.0831390	+	0.0697619i	0.683410	−	0.730035i	$-0.260496\pi$
$541$	1.93376	+	1.62262i	0.0831390	+	0.0697619i	−0.600271	+	0.799797i	$0.704941\pi$
$542$	−12.7751	−	10.7196i	−0.548739	−	0.460447i
$543$	4.28312	+	7.41858i	0.183806	+	0.318362i
$544$	4.65910	−	8.06980i	0.199757	−	0.345990i
$545$	−17.5351	+	6.38225i	−0.751120	+	0.273385i
$546$	−0.807934	−	4.58202i	−0.0345764	−	0.196092i
$547$	−1.33275	+	7.55839i	−0.0569842	+	0.323174i	−0.999953	−	0.00970799i	$-0.996910\pi$
$547$	−1.33275	+	7.55839i	−0.0569842	+	0.323174i	0.942969	+	0.332881i	$0.108021\pi$
$548$	22.5236	+	8.19793i	0.962162	+	0.350198i
$549$	−9.13500	+	7.66518i	−0.389872	+	0.327142i
$550$	−4.23442			−0.180556
$551$		0			0
$552$	−2.65539			−0.113021
$553$	−10.0248	+	8.41182i	−0.426298	+	0.357707i
$554$	11.3738	+	4.13971i	0.483225	+	0.175879i
$555$	0.195937	−	1.11121i	0.00831706	−	0.0471684i
$556$	−3.27972	−	18.6002i	−0.139091	−	0.788824i
$557$	−3.05943	+	1.11354i	−0.129632	+	0.0471823i	−0.406022	−	0.913863i	$-0.633084\pi$
$557$	−3.05943	+	1.11354i	−0.129632	+	0.0471823i	0.276389	+	0.961046i	$0.410862\pi$
$558$	2.32177	−	4.02142i	0.0982882	−	0.170240i
$559$	−12.6998	−	21.9967i	−0.537145	−	0.930362i
$560$	−0.152704	−	0.128134i	−0.00645291	−	0.00541463i
$561$	−2.29813	−	1.92836i	−0.0970273	−	0.0814155i
$562$	−5.76486	−	9.98503i	−0.243176	−	0.421193i
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	−0.805280	−	0.592895i	$-0.797985\pi$
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	0.916102	+	0.400946i	$0.131318\pi$
$564$	−0.439693	+	0.160035i	−0.0185144	+	0.00673869i
$565$	3.24376	+	18.3963i	0.136466	+	0.773936i
$566$	2.65358	−	15.0492i	0.111538	−	0.632565i
$567$	11.5360	+	4.19875i	0.484465	+	0.176331i
$568$	29.9067	−	25.0947i	1.25486	−	1.05295i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	−16.9611	+	14.2321i	−0.709179	+	0.595072i
$573$	9.47431	+	3.44837i	0.395795	+	0.144058i
$574$	1.28864	−	7.30823i	0.0537867	−	0.305040i
$575$	0.431074	+	2.44474i	0.0179770	+	0.101953i
$576$	12.8721	−	4.68507i	0.536338	−	0.195211i
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$	−6.27379	−	10.8665i	−0.260955	−	0.451987i
$579$	5.25877	+	4.41263i	0.218547	+	0.183383i
$580$	8.25150	+	6.92383i	0.342625	+	0.287496i
$581$	2.36097	+	4.08931i	0.0979494	+	0.169653i
$582$	−0.426489	+	0.738700i	−0.0176785	+	0.0306201i
$583$	−19.5744	+	7.12452i	−0.810691	+	0.295067i
$584$	−3.70409	−	21.0069i	−0.153276	−	0.869273i
$585$	6.32042	−	35.8449i	0.261317	−	1.48200i
$586$	−12.8944	−	4.69318i	−0.532663	−	0.193873i
$587$	−18.4133	+	15.4506i	−0.759998	+	0.637714i	−0.938126	−	0.346293i	$-0.887440\pi$
$587$	−18.4133	+	15.4506i	−0.759998	+	0.637714i	0.178129	+	0.984007i	$0.442996\pi$
$588$	−2.26352			−0.0933459
$589$		0			0
$590$	23.9564			0.986268
$591$	9.45652	−	7.93496i	0.388989	−	0.326401i
$592$	0.0329662	+	0.0119987i	0.00135490	+	0.000493145i
$593$	−0.736482	+	4.17680i	−0.0302437	+	0.171520i	−0.996188	−	0.0872283i	$-0.972199\pi$
$593$	−0.736482	+	4.17680i	−0.0302437	+	0.171520i	0.965945	+	0.258749i	$0.0833102\pi$
$594$	−1.58466	−	8.98703i	−0.0650192	−	0.368742i
$595$	−7.39053	+	2.68993i	−0.302982	+	0.110276i
$596$	−2.31016	+	4.00131i	−0.0946276	+	0.163900i
$597$	2.45336	+	4.24935i	0.100409	+	0.173914i
$598$	−6.26857	−	5.25996i	−0.256341	−	0.215096i
$599$	20.1270	+	16.8886i	0.822367	+	0.690048i	0.953525	−	0.301313i	$-0.0974250\pi$
$599$	20.1270	+	16.8886i	0.822367	+	0.690048i	−0.131158	+	0.991362i	$0.541869\pi$
$600$	1.06552	+	1.84554i	0.0434998	+	0.0753438i
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	0.00899659	+	0.999960i	$0.497136\pi$
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	−0.870489	+	0.492188i	$0.836197\pi$
$602$	−7.45558	+	2.71361i	−0.303867	+	0.110599i
$603$	6.70502	+	38.0261i	0.273050	+	1.54854i
$604$	−3.10917	+	17.6330i	−0.126510	+	0.717475i
$605$	1.51842	+	0.552659i	0.0617325	+	0.0224688i
$606$	−2.83931	+	2.38246i	−0.115339	+	0.0967809i
$607$	22.0969			0.896885			0.448443	−	0.893812i	$-0.351979\pi$
$607$	22.0969			0.896885			0.448443	+	0.893812i	$0.351979\pi$
$608$		0			0
$609$	3.46791			0.140527
$610$	7.48680	−	6.28217i	0.303132	−	0.254358i
$611$	−3.56418	−	1.29725i	−0.144191	−	0.0524813i
$612$	0.956462	−	5.42437i	0.0386627	−	0.219267i
$613$	1.24628	+	7.06802i	0.0503369	+	0.285474i	0.999577	−	0.0290773i	$-0.00925690\pi$
$613$	1.24628	+	7.06802i	0.0503369	+	0.285474i	−0.949240	+	0.314552i	$0.898146\pi$
$614$	−17.7833	+	6.47258i	−0.717675	+	0.261212i
$615$	−3.02481	+	5.23913i	−0.121972	+	0.211262i
$616$	9.09627	+	15.7552i	0.366499	+	0.634795i
$617$	−37.8218	−	31.7363i	−1.52265	−	1.27765i	−0.832569	−	0.553922i	$-0.813131\pi$
$617$	−37.8218	−	31.7363i	−1.52265	−	1.27765i	−0.690081	−	0.723733i	$-0.742425\pi$
$618$	0.00521457	+	0.00437554i	0.000209761	+	0.000176010i
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	−0.999279	−	0.0379684i	$-0.987911\pi$
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	0.466758	−	0.884385i	$-0.345422\pi$
$620$	3.01842	−	5.22805i	0.121223	−	0.209964i
$621$	−5.02734	+	1.82980i	−0.201740	+	0.0734274i
$622$	−2.21348	−	12.5533i	−0.0887524	−	0.503340i
$623$	−0.745100	+	4.22567i	−0.0298518	+	0.169298i
$624$	−0.110815	−	0.0403332i	−0.00443613	−	0.00161462i
$625$	−23.0312	+	19.3255i	−0.921248	+	0.773019i
$626$	−17.1643			−0.686022
$627$		0			0
$628$	12.7264			0.507838
$629$	1.06031	−	0.889704i	0.0422772	−	0.0354748i
$630$	−10.6839	−	3.88863i	−0.425657	−	0.154927i
$631$	5.78611	−	32.8147i	0.230341	−	1.30633i	−0.621864	−	0.783125i	$-0.713625\pi$
$631$	5.78611	−	32.8147i	0.230341	−	1.30633i	0.852206	−	0.523206i	$-0.175264\pi$
$632$	3.43093	+	19.4578i	0.136475	+	0.773989i
$633$	−7.31180	+	2.66128i	−0.290618	+	0.105776i
$634$	−12.4641	+	21.5884i	−0.495013	+	0.857387i
$635$	0.127889	+	0.221510i	0.00507511	+	0.00879035i
$636$	3.05303	+	2.56180i	0.121061	+	0.101582i
$637$	−14.0556	−	11.7940i	−0.556902	−	0.467296i
$638$	5.20187	+	9.00990i	0.205944	+	0.356705i
$639$	18.6905	−	32.3729i	0.739384	−	1.28065i
$640$	16.2811	−	5.92582i	0.643565	−	0.234239i
$641$	0.0236329	+	0.134029i	0.000933443	+	0.00529382i	0.985271	−	0.171001i	$-0.0547000\pi$
$641$	0.0236329	+	0.134029i	0.000933443	+	0.00529382i	−0.984337	+	0.176294i	$0.943589\pi$
$642$	0.288800	−	1.63787i	0.0113980	−	0.0646414i
$643$	−45.2725	−	16.4778i	−1.78537	−	0.649823i	−0.999506	−	0.0314270i	$-0.989995\pi$
$643$	−45.2725	−	16.4778i	−1.78537	−	0.649823i	−0.785867	−	0.618396i	$-0.787783\pi$
$644$	3.10607	−	2.60630i	0.122396	−	0.102703i
$645$	6.46791			0.254674
$646$		0			0
$647$	−36.9718			−1.45351			−0.726756	−	0.686895i	$-0.758973\pi$
$647$	−36.9718			−1.45351			−0.726756	+	0.686895i	$0.758973\pi$
$648$	14.1985	−	11.9139i	0.557768	−	0.468023i
$649$	−34.4898	−	12.5533i	−1.35384	−	0.492758i
$650$	−1.14038	+	6.46740i	−0.0447293	+	0.253672i
$651$	−0.337496	−	1.91404i	−0.0132275	−	0.0750170i
$652$	−2.33110	+	0.848451i	−0.0912929	+	0.0332279i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	1.72416	+	2.98632i	0.0674198	+	0.116775i
$655$	5.89053	+	4.94274i	0.230162	+	0.193129i
$656$	−0.144086	−	0.120902i	−0.00562559	−	0.00472043i
$657$	−10.2121	−	17.6879i	−0.398413	−	0.690072i
$658$	−0.592396	+	1.02606i	−0.0230940	+	0.0400000i
$659$	17.7366	−	6.45561i	0.690922	−	0.251475i	0.0273918	−	0.999625i	$-0.491280\pi$
$659$	17.7366	−	6.45561i	0.690922	−	0.251475i	0.663530	+	0.748150i	$0.269058\pi$
$660$	−0.979055	−	5.55250i	−0.0381097	−	0.216131i
$661$	5.31567	−	30.1467i	0.206756	−	1.17257i	−0.687897	−	0.725808i	$-0.741466\pi$
$661$	5.31567	−	30.1467i	0.206756	−	1.17257i	0.894653	−	0.446762i	$-0.147423\pi$
$662$	1.41312	+	0.514335i	0.0549226	+	0.0199902i
$663$	−3.56418	+	2.99070i	−0.138421	+	0.116149i
$664$	7.12918			0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	4.67230	−	3.92053i	0.180912	−	0.151803i
$668$	26.8081	+	9.75735i	1.03724	+	0.377523i
$669$	−0.278533	+	1.57964i	−0.0107687	+	0.0610724i
$670$	−5.49525	−	31.1651i	−0.212300	−	1.20401i
$671$	−14.0706	+	5.12127i	−0.543188	+	0.197704i
$672$	2.81908	−	4.88279i	0.108748	−	0.188358i
$673$	5.95471	+	10.3139i	0.229537	+	0.397570i	0.957671	−	0.287865i	$-0.0929454\pi$
$673$	5.95471	+	10.3139i	0.229537	+	0.397570i	−0.728134	+	0.685435i	$0.759612\pi$
$674$	17.1368	+	14.3795i	0.660085	+	0.553877i
$675$	3.28905	+	2.75984i	0.126596	+	0.106226i
$676$	9.19594	+	15.9278i	0.353690	+	0.612609i
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	−0.805119	−	0.593114i	$-0.797898\pi$
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	0.916211	+	0.400696i	$0.131232\pi$
$678$	3.24376	−	1.18063i	0.124576	−	0.0453418i
$679$	−0.594922	−	3.37397i	−0.0228310	−	0.129481i
$680$	−2.06196	+	11.6939i	−0.0790724	+	0.448442i
$681$	6.86097	+	2.49719i	0.262913	+	0.0956924i
$682$	4.46657	−	3.74789i	0.171034	−	0.143514i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$	−13.2528	+	11.1205i	−0.505996	+	0.424581i
$687$	4.70708	+	1.71324i	0.179586	+	0.0653641i
$688$	−0.0349198	+	0.198040i	−0.00133131	+	0.00755021i
$689$	5.60994	+	31.8155i	0.213722	+	1.21208i
$690$	1.95811	−	0.712694i	0.0745440	−	0.0271318i
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	−0.361744	−	0.932278i	$-0.617818\pi$
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	0.988248	−	0.152860i	$-0.0488483\pi$
$692$	−0.549935	−	0.952515i	−0.0209054	−	0.0362092i
$693$	13.3439	+	11.1969i	0.506893	+	0.425333i
$694$	−5.18866	−	4.35381i	−0.196959	−	0.165268i
$695$	19.4932	+	33.7632i	0.739419	+	1.28071i
$696$	2.61793	−	4.53438i	0.0992322	−	0.171875i
$697$	−6.97343	+	2.53812i	−0.264138	+	0.0961382i
$698$	−3.47508	−	19.7082i	−0.131534	−	0.745965i
$699$	2.23467	−	12.6734i	0.0845230	−	0.479354i
$700$	−3.05778	−	1.11294i	−0.115573	−	0.0420652i
$701$	16.3607	−	13.7283i	0.617936	−	0.518510i	−0.279218	−	0.960228i	$-0.590075\pi$
$701$	16.3607	−	13.7283i	0.617936	−	0.518510i	0.897154	+	0.441718i	$0.145631\pi$
$702$	−14.1530			−0.534171
$703$		0			0
$704$	17.2003			0.648260
$705$	0.739885	−	0.620838i	0.0278657	−	0.0233821i
$706$	−9.45811	−	3.44247i	−0.355961	−	0.129559i
$707$	2.58512	−	14.6610i	0.0972235	−	0.551382i
$708$	1.21941	+	6.91560i	0.0458281	+	0.259904i
$709$	14.8195	−	5.39387i	0.556560	−	0.202571i	−0.0483989	−	0.998828i	$-0.515412\pi$
$709$	14.8195	−	5.39387i	0.556560	−	0.202571i	0.604959	+	0.796257i	$0.293190\pi$
$710$	−15.3182	+	26.5319i	−0.574882	+	0.995725i
$711$	9.45904	+	16.3835i	0.354742	+	0.614431i
$712$	4.96270	+	4.16420i	0.185985	+	0.156060i
$713$	−2.61856	−	2.19723i	−0.0980657	−	0.0822869i
$714$	0.726682	+	1.25865i	0.0271954	+	0.0471038i
$715$	22.8516	−	39.5802i	0.854603	−	1.48022i
$716$	24.5736	−	8.94405i	0.918357	−	0.334255i
$717$	2.15523	+	12.2229i	0.0804885	+	0.456473i
$718$	−1.58569	+	8.99292i	−0.0591776	+	0.335613i
$719$	33.1977	+	12.0830i	1.23807	+	0.450620i	0.876353	−	0.481669i	$-0.159969\pi$
$719$	33.1977	+	12.0830i	1.23807	+	0.450620i	0.361714	+	0.932289i	$0.382192\pi$
$720$	−0.220752	+	0.185233i	−0.00822693	+	0.00690322i
$721$	−0.0273411			−0.00101824
$722$		0			0
$723$	0.158385			0.00589040
$724$	−15.1284	+	12.6942i	−0.562241	+	0.471776i
$725$	−4.59967	−	1.67414i	−0.170827	−	0.0621761i
$726$	0.0518514	−	0.294064i	0.00192438	−	0.0109137i
$727$	7.01913	+	39.8075i	0.260325	+	1.47638i	0.782024	+	0.623248i	$0.214187\pi$
$727$	7.01913	+	39.8075i	0.260325	+	1.47638i	−0.521699	+	0.853130i	$0.674702\pi$
$728$	26.5133	−	9.65004i	0.982647	−	0.357654i
$729$	6.44562	−	11.1641i	0.238727	−	0.413487i
$730$	8.36959	+	14.4965i	0.309772	+	0.536541i
$731$	6.07785	+	5.09992i	0.224797	+	0.188627i
$732$	2.19459	+	1.84148i	0.0811145	+	0.0680631i
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$	−14.3045	+	24.7762i	−0.527990	+	0.914505i
$735$	4.39053	−	1.59802i	0.161947	−	0.0589439i
$736$	−1.72193	−	9.76557i	−0.0634713	−	0.359964i
$737$	−8.41921	+	47.7477i	−0.310126	+	1.75881i
$738$	−10.0809	−	3.66916i	−0.371085	−	0.135064i
$739$	−15.8387	+	13.2902i	−0.582635	+	0.488889i	−0.885811	−	0.464046i	$-0.846397\pi$
$739$	−15.8387	+	13.2902i	−0.582635	+	0.488889i	0.303176	+	0.952935i	$0.401953\pi$
$740$	2.60132			0.0956264
$741$		0			0
$742$	10.0915			0.370471
$743$	−5.13563	+	4.30930i	−0.188408	+	0.158093i	−0.732113	−	0.681183i	$-0.761466\pi$
$743$	−5.13563	+	4.30930i	−0.188408	+	0.158093i	0.543705	+	0.839277i	$0.317021\pi$
$744$	−2.75743	−	1.00362i	−0.101092	−	0.0367945i
$745$	1.65611	−	9.39225i	0.0606751	−	0.344105i
$746$	4.65529	+	26.4014i	0.170442	+	0.966625i
$747$	6.41447	−	2.33468i	0.234693	−	0.0854213i
$748$	3.45811	−	5.98962i	0.126441	−	0.219002i
$749$	3.34002	+	5.78509i	0.122042	+	0.211383i
$750$	3.25696	+	2.73291i	0.118927	+	0.0997919i
$751$	−8.20233	−	6.88258i	−0.299307	−	0.251149i	0.480749	−	0.876859i	$-0.340365\pi$
$751$	−8.20233	−	6.88258i	−0.299307	−	0.251149i	−0.780056	+	0.625710i	$0.784809\pi$
$752$	0.0150147	+	0.0260063i	0.000547531	+	0.000948352i
$753$	−4.30928	+	7.46389i	−0.157039	+	0.271999i
$754$	15.1621	−	5.51855i	0.552171	−	0.200974i
$755$	−6.41787	−	36.3976i	−0.233570	−	1.32464i
$756$	1.21776	−	6.90625i	0.0442895	−	0.251178i
$757$	3.81743	+	1.38943i	0.138747	+	0.0504997i	0.410460	−	0.911878i	$-0.365368\pi$
$757$	3.81743	+	1.38943i	0.138747	+	0.0504997i	−0.271713	+	0.962378i	$0.587590\pi$
$758$	12.0312	−	10.0954i	0.436993	−	0.366681i
$759$	−3.19253			−0.115882
$760$		0			0
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$	0.0362077	−	0.0303818i	0.00131167	−	0.00110062i
$763$	−13.0150	−	4.73708i	−0.471175	−	0.171494i
$764$	−4.03626	+	22.8908i	−0.146027	+	0.828160i
$765$	1.97431	+	11.1969i	0.0713812	+	0.404823i
$766$	19.3830	−	7.05482i	0.700334	−	0.254901i
$767$	−28.4616	+	49.2969i	−1.02769	+	1.78001i
$768$	−4.28359	−	7.41939i	−0.154571	−	0.267724i
$769$	16.3530	+	13.7218i	0.589703	+	0.494820i	0.888117	−	0.459617i	$-0.152013\pi$
$769$	16.3530	+	13.7218i	0.589703	+	0.494820i	−0.298414	+	0.954437i	$0.596458\pi$
$770$	−10.9363	−	9.17664i	−0.394117	−	0.330703i
$771$	−4.08512	−	7.07564i	−0.147122	−	0.254823i
$772$	−7.91312	+	13.7059i	−0.284800	+	0.493287i
$773$	16.8366	−	6.12803i	0.605571	−	0.220410i	−0.0209932	−	0.999780i	$-0.506683\pi$
$773$	16.8366	−	6.12803i	0.605571	−	0.220410i	0.626564	+	0.779370i	$0.284461\pi$
$774$	1.99169	+	11.2954i	0.0715897	+	0.406005i
$775$	−0.476367	+	2.70161i	−0.0171116	+	0.0970448i
$776$	−4.86066	−	1.76914i	−0.174488	−	0.0635083i
$777$	0.641559	−	0.538332i	0.0230158	−	0.0193126i
$778$	−3.43788			−0.123254
$779$		0			0
$780$	−8.74422			−0.313093
$781$	35.9564	−	30.1710i	1.28662	−	1.07960i
$782$	2.40198	+	0.874249i	0.0858946	+	0.0312631i
$783$	1.83181	−	10.3887i	0.0654637	−	0.371263i
$784$	0.0252254	+	0.143061i	0.000900909	+	0.00510931i
$785$	−24.6853	+	8.98470i	−0.881055	+	0.320678i
$786$	0.710485	−	1.23060i	0.0253422	−	0.0438939i
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.861656	+	0.507493i	$0.169428\pi$
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.00867371	+	0.999962i	$0.497239\pi$
$788$	21.8011	+	18.2933i	0.776633	+	0.651672i
$789$	−3.93061	−	3.29817i	−0.139933	−	0.117418i
$790$	−7.75237	−	13.4275i	−0.275817	−	0.477729i
$791$	−6.93242	+	12.0073i	−0.246488	+	0.426930i
$792$	24.7135	−	8.99497i	0.878155	−	0.319622i
$793$	4.03256	+	22.8698i	0.143200	+	0.812129i
$794$	−1.36808	+	7.75876i	−0.0485513	+	0.275348i
$795$	−7.73055	−	2.81369i	−0.274174	−	0.0997913i
$796$	−8.66550	+	7.27122i	−0.307140	+	0.257721i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	−6.09627	+	5.11538i	−0.215536	+	0.180856i
$801$	5.82888	+	2.12154i	0.205953	+	0.0749609i
$802$	−0.309582	+	1.75573i	−0.0109317	+	0.0619969i
$803$	−4.45336	−	25.2563i	−0.157156	−	0.891275i
$804$	8.71688	−	3.17269i	0.307421	−	0.111892i
$805$	−4.18479	+	7.24827i	−0.147495	+	0.255468i
$806$	−4.52141	−	7.83131i	−0.159260	−	0.275846i
$807$	−7.45059	−	6.25179i	−0.262273	−	0.220073i
$808$	−17.2181	−	14.4477i	−0.605729	−	0.508267i
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	0.966459	−	0.256822i	$-0.0826755\pi$
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	−0.705644	+	0.708567i	$0.749342\pi$
$810$	−7.27244	+	12.5962i	−0.255528	+	0.442587i
$811$	−7.87211	+	2.86521i	−0.276427	+	0.100611i	−0.476514	−	0.879167i	$-0.658100\pi$
$811$	−7.87211	+	2.86521i	−0.276427	+	0.100611i	0.200087	+	0.979778i	$0.435878\pi$
$812$	1.38831	+	7.87349i	0.0487201	+	0.276305i
$813$	−1.75221	+	9.93729i	−0.0614527	+	0.348516i
$814$	2.36097	+	0.859322i	0.0827518	+	0.0301192i
$815$	3.92262	−	3.29147i	0.137403	−	0.115295i
$816$	0.0368366			0.00128954
$817$		0			0
$818$	−28.3233			−0.990299
$819$	20.6951	−	17.3652i	0.723144	−	0.606790i
$820$	−13.1058	−	4.77011i	−0.457673	−	0.166579i
$821$	1.09034	−	6.18361i	0.0380530	−	0.215809i	−0.959852	−	0.280507i	$-0.909497\pi$
$821$	1.09034	−	6.18361i	0.0380530	−	0.215809i	0.997905	+	0.0646980i	$0.0206084\pi$
$822$	1.58765	+	9.00400i	0.0553756	+	0.314051i
$823$	−10.3614	+	3.77125i	−0.361177	+	0.131458i	−0.516233	−	0.856448i	$-0.672666\pi$
$823$	−10.3614	+	3.77125i	−0.361177	+	0.131458i	0.155056	+	0.987906i	$0.450444\pi$
$824$	−0.0206398	+	0.0357492i	−0.000719023	+	0.00124538i
$825$	1.28106	+	2.21886i	0.0446008	+	0.0772508i
$826$	13.6211	+	11.4294i	0.473938	+	0.397681i
$827$	−25.9963	−	21.8135i	−0.903982	−	0.758531i	0.0669829	−	0.997754i	$-0.478663\pi$
$827$	−25.9963	−	21.8135i	−0.903982	−	0.758531i	−0.970965	+	0.239223i	$0.923107\pi$
$828$	−2.93077	−	5.07624i	−0.101851	−	0.176412i
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	−0.986892	−	0.161381i	$-0.948405\pi$
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	0.633206	+	0.773983i	$0.281738\pi$
$830$	−5.25712	+	1.91344i	−0.182477	+	0.0664163i
$831$	−1.27173	−	7.21232i	−0.0441157	−	0.250192i
$832$	4.63223	−	26.2707i	0.160594	−	0.910771i
$833$	5.38578	+	1.96026i	0.186606	+	0.0679191i
$834$	5.51889	−	4.63089i	0.191103	−	0.160355i
$835$	−58.8881			−2.03791
$836$		0			0
$837$	−5.91210			−0.204352
$838$	15.6623	−	13.1422i	0.541044	−	0.453990i
$839$	14.8559	+	5.40711i	0.512883	+	0.186674i	0.585480	−	0.810687i	$-0.300906\pi$
$839$	14.8559	+	5.40711i	0.512883	+	0.186674i	−0.0725964	+	0.997361i	$0.523128\pi$
$840$	−1.24763	+	7.07564i	−0.0430472	+	0.244133i
$841$	−2.94743	−	16.7157i	−0.101636	−	0.576404i
$842$	−5.33275	+	1.94096i	−0.183779	+	0.0668900i
$843$	−3.48814	+	6.04164i	−0.120138	+	0.208085i
$844$	−8.96926	−	15.5352i	−0.308734	−	0.534744i
$845$	−29.0822	−	24.4029i	−1.00046	−	0.839484i
$846$	1.31205	+	1.10094i	0.0451093	+	0.0378512i
$847$	0.599670	+	1.03866i	0.0206049	+	0.0356888i
$848$	0.127889	−	0.221510i	0.00439172	−	0.00760668i
$849$	−8.68866	+	3.16241i	−0.298194	+	0.108534i
$850$	−0.356219	−	2.02022i	−0.0122182	−	0.0692930i
$851$	0.255777	−	1.45059i	0.00876794	−	0.0497254i
$852$	−8.43882	−	3.07148i	−0.289109	−	0.105227i
$853$	−40.3316	+	33.8422i	−1.38093	+	1.15874i	−0.412061	+	0.911156i	$0.635191\pi$
$853$	−40.3316	+	33.8422i	−1.38093	+	1.15874i	−0.968867	+	0.247580i	$0.920365\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	17.6400	−	14.8017i	0.602570	−	0.505616i	−0.289701	−	0.957117i	$-0.593556\pi$
$857$	17.6400	−	14.8017i	0.602570	−	0.505616i	0.892271	+	0.451501i	$0.149111\pi$
$858$	−7.93629	−	2.88857i	−0.270940	−	0.0986143i
$859$	1.54710	−	8.77406i	0.0527865	−	0.299367i	−0.946973	−	0.321314i	$-0.895875\pi$
$859$	1.54710	−	8.77406i	0.0527865	−	0.299367i	0.999759	+	0.0219471i	$0.00698655\pi$
$860$	2.58930	+	14.6846i	0.0882943	+	0.500742i
$861$	−4.21941	+	1.53574i	−0.143797	+	0.0523378i
$862$	6.15451	−	10.6599i	0.209624	−	0.363079i
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	0.999970	+	0.00773998i	$0.00246374\pi$
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	−0.493282	+	0.869869i	$0.664203\pi$
$864$	−13.1382	−	11.0242i	−0.446969	−	0.375052i
$865$	1.73917	+	1.45934i	0.0591336	+	0.0496189i
$866$	12.6160	+	21.8516i	0.428710	+	0.742548i
$867$	−3.79607	+	6.57499i	−0.128921	+	0.223298i
$868$	4.21048	−	1.53249i	0.142913	−	0.0520161i
$869$	4.12495	+	23.3938i	0.139929	+	0.793579i
$870$	−0.713478	+	4.04633i	−0.0241892	+	0.137184i
$871$	70.6596	+	25.7180i	2.39421	+	0.871421i
$872$	−16.0189	+	13.4414i	−0.542468	+	0.455185i
$873$	−4.95273			−0.167625
$874$		0			0
$875$	−17.0770			−0.577307
$876$	−3.75877	+	3.15398i	−0.126997	+	0.106563i
$877$	−23.5205	−	8.56077i	−0.794232	−	0.289077i	−0.0871379	−	0.996196i	$-0.527772\pi$
$877$	−23.5205	−	8.56077i	−0.794232	−	0.289077i	−0.707094	+	0.707119i	$0.749994\pi$
$878$	−2.03741	+	11.5547i	−0.0687592	+	0.389953i
$879$	1.44175	+	8.17658i	0.0486291	+	0.275789i
$880$	−0.340022	+	0.123758i	−0.0114622	+	0.00417188i
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	−0.985095	−	0.172014i	$-0.944973\pi$
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$882$	4.14274	+	7.17544i	0.139493	+	0.241610i
$883$	−8.14156	−	6.83158i	−0.273985	−	0.229901i	0.495433	−	0.868646i	$-0.335009\pi$
$883$	−8.14156	−	6.83158i	−0.273985	−	0.229901i	−0.769418	+	0.638745i	$0.779454\pi$
$884$	−8.21688	−	6.89478i	−0.276364	−	0.231897i
$885$	−7.24763	−	12.5533i	−0.243626	−	0.421973i
$886$	14.8981	−	25.8043i	0.500512	−	0.866912i
$887$	−52.9411	+	19.2690i	−1.77759	+	0.646989i	−0.777758	+	0.628564i	$0.783643\pi$
$887$	−52.9411	+	19.2690i	−1.77759	+	0.646989i	−0.999830	+	0.0184249i	$0.994135\pi$
$888$	−0.219570	−	1.24524i	−0.00736828	−	0.0417876i
$889$	−0.0329662	+	0.186961i	−0.00110565	+	0.00627046i
$890$	−4.77719	−	1.73875i	−0.160132	−	0.0582832i
$891$	17.0706	−	14.3239i	0.571886	−	0.479869i
$892$	−3.69789			−0.123815
$893$		0			0
$894$	−1.76239			−0.0589432
$895$	−41.3508	+	34.6974i	−1.38220	+	1.15981i
$896$	12.0842	+	4.39831i	0.403706	+	0.146937i
$897$	−0.859785	+	4.87608i	−0.0287074	+	0.162808i
$898$	2.87696	+	16.3161i	0.0960056	+	0.544475i
$899$	6.33363	−	2.30525i	0.211238	−	0.0768844i
$900$	−2.35204	+	4.07386i	−0.0784015	+	0.135795i
$901$	−5.04576	−	8.73951i	−0.168099	−	0.291155i
$902$	−10.3191	−	8.65873i	−0.343588	−	0.288304i
$903$	3.67752	+	3.08580i	0.122380	+	0.102689i
$904$	10.4666	+	18.1286i	0.348113	+	0.602949i
$905$	20.3824	−	35.3033i	0.677533	−	1.17352i
$906$	−6.41787	+	2.33591i	−0.213219	+	0.0776055i
$907$	1.02863	+	5.83365i	0.0341551	+	0.193703i	0.997111	−	0.0759549i	$-0.0242005\pi$
$907$	1.02863	+	5.83365i	0.0341551	+	0.193703i	−0.962956	+	0.269658i	$0.913089\pi$
$908$	−2.92292	+	16.5767i	−0.0970006	+	0.550118i
$909$	−20.2233	−	7.36067i	−0.670764	−	0.244138i
$910$	−16.9611	+	14.2321i	−0.562255	+	0.471788i
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$	−9.61902	+	8.07132i	−0.318169	+	0.266975i
$915$	−5.55690	−	2.02255i	−0.183706	−	0.0668634i
$916$	−2.00532	+	11.3727i	−0.0662577	+	0.375766i
$917$	0.991077	+	5.62068i	0.0327283	+	0.185611i
$918$	4.15435	−	1.51206i	0.137114	−	0.0499054i
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	−0.809637	−	0.586931i	$-0.800336\pi$
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	0.913116	+	0.407700i	$0.133669\pi$
$920$	6.31820	+	10.9434i	0.208305	+	0.360795i
$921$	8.77173	+	7.36035i	0.289038	+	0.242532i
$922$	9.38263	+	7.87296i	0.309000	+	0.259282i
$923$	−36.3979	−	63.0429i	−1.19805	−	2.07508i
$924$	2.09240	−	3.62414i	0.0688348	−	0.119225i
$925$	−1.11081	+	0.404303i	−0.0365234	+	0.0132934i
$926$	0.269200	+	1.52671i	0.00884645	+	0.0501707i
$927$	−0.00686344	+	0.0389245i	−0.000225425	+	0.00127845i
$928$	18.3735	+	6.68739i	0.603138	+	0.219524i
$929$	21.6969	−	18.2058i	0.711851	−	0.597314i	−0.213267	−	0.976994i	$-0.568410\pi$
$929$	21.6969	−	18.2058i	0.711851	−	0.597314i	0.925118	+	0.379680i	$0.123966\pi$
$930$	2.30272			0.0755091
$931$		0			0
$932$	29.6682			0.971814
$933$	−5.90832	+	4.95767i	−0.193430	+	0.162307i
$934$	18.2144	+	6.62948i	0.595992	+	0.216923i
$935$	−2.47906	+	14.0594i	−0.0810738	+	0.459792i
$936$	−7.08276	−	40.1683i	−0.231507	−	1.31294i
$937$	18.8614	−	6.86500i	0.616176	−	0.224270i	−0.0150273	−	0.999887i	$-0.504784\pi$
$937$	18.8614	−	6.86500i	0.616176	−	0.224270i	0.631203	+	0.775617i	$0.282561\pi$
$938$	11.7442	−	20.3416i	0.383462	−	0.664176i
$939$	5.19278	+	8.99416i	0.169460	+	0.293513i
$940$	1.70574	+	1.43128i	0.0556350	+	0.0466833i
$941$	−4.13294	−	3.46795i	−0.134730	−	0.113052i	0.572932	−	0.819603i	$-0.305806\pi$
$941$	−4.13294	−	3.46795i	−0.134730	−	0.113052i	−0.707662	+	0.706551i	$0.750250\pi$
$942$	2.42720	+	4.20404i	0.0790826	+	0.136975i
$943$	−3.94862	+	6.83920i	−0.128585	+	0.222715i
$944$	0.423496	−	0.154140i	0.0137836	−	0.00501683i
$945$	2.51367	+	14.2557i	0.0817697	+	0.463739i
$946$	−2.50088	+	14.1832i	−0.0813105	+	0.461135i
$947$	−6.24257	−	2.27211i	−0.202856	−	0.0738337i	0.238594	−	0.971119i	$-0.423314\pi$
$947$	−6.24257	−	2.27211i	−0.202856	−	0.0738337i	−0.441450	+	0.897286i	$0.645536\pi$
$948$	3.48158	−	2.92139i	0.113077	−	0.0948825i
$949$	−39.7743			−1.29113
$950$		0			0
$951$	15.0833			0.489109
$952$	−6.75150	+	5.66518i	−0.218817	+	0.183609i
$953$	−13.9299	−	5.07007i	−0.451233	−	0.164236i	0.106399	−	0.994324i	$-0.466068\pi$
$953$	−13.9299	−	5.07007i	−0.451233	−	0.164236i	−0.557632	+	0.830088i	$0.688290\pi$
$954$	2.53327	−	14.3669i	0.0820177	−	0.465145i
$955$	−8.33157	−	47.2507i	−0.269603	−	1.52900i
$956$	−26.8879	+	9.78639i	−0.869617	+	0.316515i
$957$	3.14749	−	5.45161i	0.101744	−	0.176226i
$958$	−11.1932	−	19.3873i	−0.361637	−	0.626374i
$959$	−28.1313	−	23.6050i	−0.908409	−	0.762245i
$960$	5.20368	+	4.36640i	0.167948	+	0.140925i
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$	1.94831	−	3.37457i	0.0628161	−	0.108801i
$963$	9.07444	−	3.30283i	0.292420	−	0.106432i
$964$	0.0634062	+	0.359595i	0.00204218	+	0.0115818i
$965$	5.67277	−	32.1719i	0.182613	−	1.03565i
$966$	1.45336	+	0.528981i	0.0467612	+	0.0170197i
$967$	16.2567	−	13.6410i	0.522781	−	0.438665i	−0.342819	−	0.939401i	$-0.611382\pi$
$967$	16.2567	−	13.6410i	0.522781	−	0.438665i	0.865600	+	0.500736i	$0.166937\pi$
$968$	1.81076			0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	28.8084	−	24.1731i	0.924506	−	0.775752i	−0.0503172	−	0.998733i	$-0.516023\pi$
$971$	28.8084	−	24.1731i	0.924506	−	0.775752i	0.974823	+	0.222981i	$0.0715788\pi$
$972$	−14.5256	−	5.28688i	−0.465908	−	0.169577i
$973$	−5.02481	+	28.4971i	−0.161088	+	0.913576i
$974$	−3.43747	−	19.4949i	−0.110144	−	0.624656i
$975$	3.73396	−	1.35905i	0.119582	−	0.0435244i
$976$	0.0919294	−	0.159226i	0.00294259	−	0.00509671i
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	−0.954204	−	0.299156i	$-0.903295\pi$
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	0.218026	−	0.975943i	$-0.430038\pi$
$978$	−0.724871	−	0.608239i	−0.0231788	−	0.0194493i
$979$	5.96657	+	5.00654i	0.190692	+	0.160010i
$980$	5.38578	+	9.32845i	0.172042	+	0.297986i
$981$	−10.0111	+	17.3398i	−0.319631	+	0.553618i
$982$	12.9192	−	4.70221i	0.412269	−	0.150054i
$983$	−10.5225	−	59.6758i	−0.335614	−	1.90336i	−0.421085	−	0.907021i	$-0.638351\pi$
$983$	−10.5225	−	59.6758i	−0.335614	−	1.90336i	0.0854708	−	0.996341i	$-0.472761\pi$
$984$	−1.17721	+	6.67631i	−0.0375282	+	0.212833i
$985$	−55.2024	−	20.0920i	−1.75889	−	0.640185i
$986$	−3.86097	+	3.23974i	−0.122958	+	0.103174i
$987$	0.716881			0.0228186
$988$		0			0
$989$	8.44326			0.268480
$990$	−15.8097	+	13.2660i	−0.502467	+	0.421620i
$991$	39.3714	+	14.3300i	1.25067	+	0.455208i	0.880629	−	0.473806i	$-0.157120\pi$
$991$	39.3714	+	14.3300i	1.25067	+	0.455208i	0.370044	+	0.929014i	$0.379342\pi$
$992$	1.90286	−	10.7916i	0.0604157	−	0.342635i
$993$	−0.158004	−	0.896088i	−0.00501412	−	0.0284365i
$994$	−21.3678	+	7.77725i	−0.677746	+	0.246680i
$995$	11.6750	−	20.2217i	0.370122	−	0.641070i
$996$	−0.819955	−	1.42020i	−0.0259813	−	0.0450009i
$997$	25.8273	+	21.6717i	0.817958	+	0.686349i	0.952493	−	0.304560i	$-0.0985095\pi$
$997$	25.8273	+	21.6717i	0.817958	+	0.686349i	−0.134535	+	0.990909i	$0.542954\pi$
$998$	19.2777	+	16.1759i	0.610224	+	0.512038i
$999$	−1.27379	−	2.20626i	−0.0403008	−	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.b.234.1		6
19.2	odd	18		19.2.e.a.5.1	yes	6
19.3	odd	18		361.2.e.f.54.1		6
19.4	even	9		361.2.a.h.1.1		3
19.5	even	9		361.2.e.a.245.1		6
19.6	even	9		361.2.c.h.292.3		6
19.7	even	3		361.2.e.a.28.1		6
19.8	odd	6		19.2.e.a.4.1	✓	6
19.9	even	9		361.2.c.h.68.3		6
19.10	odd	18		361.2.c.i.68.1		6
19.11	even	3		361.2.e.h.99.1		6
19.12	odd	6		361.2.e.g.28.1		6
19.13	odd	18		361.2.c.i.292.1		6
19.14	odd	18		361.2.e.g.245.1		6
19.15	odd	18		361.2.a.g.1.3		3
19.16	even	9	inner	361.2.e.b.54.1		6
19.17	even	9		361.2.e.h.62.1		6
19.18	odd	2		361.2.e.f.234.1		6
57.2	even	18		171.2.u.c.100.1		6
57.8	even	6		171.2.u.c.118.1		6
57.23	odd	18		3249.2.a.s.1.3		3
57.53	even	18		3249.2.a.z.1.1		3
76.15	even	18		5776.2.a.br.1.1		3
76.23	odd	18		5776.2.a.bi.1.3		3
76.27	even	6		304.2.u.b.289.1		6
76.59	even	18		304.2.u.b.81.1		6
95.2	even	36		475.2.u.a.24.1		12
95.4	even	18		9025.2.a.x.1.3		3
95.8	even	12		475.2.u.a.99.1		12
95.27	even	12		475.2.u.a.99.2		12
95.34	odd	18		9025.2.a.bd.1.1		3
95.59	odd	18		475.2.l.a.176.1		6
95.78	even	36		475.2.u.a.24.2		12
95.84	odd	6		475.2.l.a.251.1		6
133.2	odd	18		931.2.v.b.214.1		6
133.27	even	6		931.2.w.a.99.1		6
133.40	even	18		931.2.v.a.214.1		6
133.46	odd	6		931.2.v.b.422.1		6
133.59	even	18		931.2.x.b.765.1		6
133.65	odd	6		931.2.x.a.802.1		6
133.97	even	18		931.2.w.a.442.1		6
133.103	even	6		931.2.x.b.802.1		6
133.116	odd	18		931.2.x.a.765.1		6
133.122	even	6		931.2.v.a.422.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	19.8	odd	6
19.2.e.a.5.1	yes	6	19.2	odd	18
171.2.u.c.100.1		6	57.2	even	18
171.2.u.c.118.1		6	57.8	even	6
304.2.u.b.81.1		6	76.59	even	18
304.2.u.b.289.1		6	76.27	even	6
361.2.a.g.1.3		3	19.15	odd	18
361.2.a.h.1.1		3	19.4	even	9
361.2.c.h.68.3		6	19.9	even	9
361.2.c.h.292.3		6	19.6	even	9
361.2.c.i.68.1		6	19.10	odd	18
361.2.c.i.292.1		6	19.13	odd	18
361.2.e.a.28.1		6	19.7	even	3
361.2.e.a.245.1		6	19.5	even	9
361.2.e.b.54.1		6	19.16	even	9	inner
361.2.e.b.234.1		6	1.1	even	1	trivial
361.2.e.f.54.1		6	19.3	odd	18
361.2.e.f.234.1		6	19.18	odd	2
361.2.e.g.28.1		6	19.12	odd	6
361.2.e.g.245.1		6	19.14	odd	18
361.2.e.h.62.1		6	19.17	even	9
361.2.e.h.99.1		6	19.11	even	3
475.2.l.a.176.1		6	95.59	odd	18
475.2.l.a.251.1		6	95.84	odd	6
475.2.u.a.24.1		12	95.2	even	36
475.2.u.a.24.2		12	95.78	even	36
475.2.u.a.99.1		12	95.8	even	12
475.2.u.a.99.2		12	95.27	even	12
931.2.v.a.214.1		6	133.40	even	18
931.2.v.a.422.1		6	133.122	even	6
931.2.v.b.214.1		6	133.2	odd	18
931.2.v.b.422.1		6	133.46	odd	6
931.2.w.a.99.1		6	133.27	even	6
931.2.w.a.442.1		6	133.97	even	18
931.2.x.a.765.1		6	133.116	odd	18
931.2.x.a.802.1		6	133.65	odd	6
931.2.x.b.765.1		6	133.59	even	18
931.2.x.b.802.1		6	133.103	even	6
3249.2.a.s.1.3		3	57.23	odd	18
3249.2.a.z.1.1		3	57.53	even	18
5776.2.a.bi.1.3		3	76.23	odd	18
5776.2.a.br.1.1		3	76.15	even	18
9025.2.a.x.1.3		3	95.4	even	18
9025.2.a.bd.1.1		3	95.34	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 + 0.565258i) q^{2} +(0.500000 + 0.181985i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(-0.439693 - 2.49362i) q^{5} +(-0.439693 + 0.160035i) q^{6} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-2.08125 - 1.74638i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(-0.326352 + 0.565258i) q^{12} +(-4.97178 + 1.80958i) q^{13} +(0.286989 + 1.62760i) q^{14} +(0.233956 - 1.32683i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(1.26604 - 1.06234i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(0.766044 - 0.642788i) q^{21} +(2.81908 + 1.02606i) q^{22} +(0.305407 - 1.73205i) q^{23} +(-0.262174 - 1.48686i) q^{24} +(-1.32635 + 0.482753i) q^{25} +(2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(1.76604 + 1.48189i) q^{28} +(2.65657 + 2.22913i) q^{29} +(0.592396 + 1.02606i) q^{30} +(0.971782 - 1.68317i) q^{31} +(5.29813 - 1.92836i) q^{32} +(-0.315207 - 1.78763i) q^{33} +(-0.252374 + 1.43128i) q^{34} +(-4.47178 - 1.62760i) q^{35} +(2.55303 - 2.14225i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(-5.50387 + 4.61830i) q^{40} +(-4.21941 - 1.53574i) q^{41} +(-0.152704 + 0.866025i) q^{42} +(0.833626 + 4.72773i) q^{43} +(3.93242 - 1.43128i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(0.773318 + 1.33943i) q^{46} +(0.549163 + 0.460802i) q^{47} +(0.0170741 + 0.0143269i) q^{48} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(0.826352 - 0.300767i) q^{51} +(-1.12701 - 6.39160i) q^{52} +(1.06031 - 6.01330i) q^{53} +(2.51367 + 0.914901i) q^{54} +(-6.61721 + 5.55250i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(8.24170 - 6.91560i) q^{59} +(1.55303 + 0.565258i) q^{60} +(0.762174 - 4.32250i) q^{61} +(0.296789 + 1.68317i) q^{62} +(-4.79813 + 1.74638i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(1.22281 + 1.02606i) q^{66} +(-10.8871 - 9.13538i) q^{67} +(1.01367 + 1.75573i) q^{68} +(0.467911 - 0.810446i) q^{69} +(3.93242 - 1.43128i) q^{70} +(2.38919 + 13.5497i) q^{71} +(-1.33868 + 7.59202i) q^{72} +(7.06418 + 2.57115i) q^{73} +(-0.564178 + 0.473401i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(1.89646 - 1.59132i) q^{78} +(-6.54323 - 2.38154i) q^{79} +(0.0184183 - 0.104455i) q^{80} +(1.13429 + 6.43285i) q^{81} +(3.71048 - 1.35051i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(0.613341 + 1.06234i) q^{84} +(-3.20574 - 2.68993i) q^{85} +(-3.23396 - 2.71361i) q^{86} +(0.922618 + 1.59802i) q^{87} +(-4.84002 + 8.38316i) q^{88} +(-2.14543 + 0.780873i) q^{89} +(-1.05051 - 5.95772i) q^{90} +(-1.72668 + 9.79250i) q^{91} +(2.02734 + 0.737892i) q^{92} +(0.792204 - 0.664738i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(1.39646 - 1.17177i) q^{97} +(-2.86571 - 1.04303i) q^{98} +(-1.60947 + 9.12776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{8} - 15 q^{9} - 3 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 9 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26}+ \cdots - 27 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^8 - 15 * q^9 - 3 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 9 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^20 + 6 * q^23 - 21 * q^24 - 9 * q^25 + 15 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 9 * q^31 + 18 * q^32 - 9 * q^33 - 18 * q^34 - 12 * q^35 + 3 * q^36 - 24 * q^39 - 9 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 - 15 * q^45 + 18 * q^46 + 15 * q^47 + 21 * q^48 + 15 * q^49 + 15 * q^50 + 6 * q^51 + 21 * q^52 + 12 * q^53 - 6 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 + 24 * q^61 - 3 * q^62 - 15 * q^63 - 12 * q^64 + 12 * q^65 + 18 * q^66 - 6 * q^67 - 15 * q^68 + 12 * q^69 + 6 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 - 30 * q^75 - 18 * q^77 + 21 * q^78 - 24 * q^79 + 12 * q^80 - 3 * q^81 + 45 * q^82 - 3 * q^84 - 9 * q^85 - 24 * q^86 - 21 * q^87 - 9 * q^88 + 3 * q^89 - 9 * q^90 + 3 * q^91 - 30 * q^92 - 36 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^97 - 27 * q^98 - 27 * q^99

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